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Search: a328308 -id:a328308
Displaying 1-10 of 15 results found. page 1 2
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A359541 Inverse Möbius transform of A328308, which is the characteristic function of numbers that eventually reach zero when iterated with the arithmetic derivative. +20
4
1, 2, 2, 2, 2, 4, 2, 2, 3, 4, 2, 4, 2, 4, 3, 2, 2, 6, 2, 4, 4, 4, 2, 4, 3, 3, 3, 4, 2, 7, 2, 2, 4, 4, 3, 6, 2, 4, 3, 4, 2, 8, 2, 4, 4, 4, 2, 4, 3, 5, 3, 3, 2, 6, 3, 4, 4, 4, 2, 7, 2, 4, 5, 2, 4, 8, 2, 4, 3, 7, 2, 6, 2, 3, 4, 4, 4, 6, 2, 4, 3, 4, 2, 8, 4, 3, 3, 4, 2, 9, 3, 4, 4, 4, 3, 4, 2, 6, 5, 5, 2, 6, 2, 3, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
FORMULA
a(n) = Sum_{d|n} A328308(d).
a(n) = A000005(n) - A359542(n).
a(n) < A328309(n).
PROG
(PARI)
A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));
A328308(n) = if(!n, 1, while(n>1, n = A003415checked(n)); (n));
A359541(n) = sumdiv(n, d, A328308(d));
CROSSREFS
Cf. A000005, A328308, A328309, A359542.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 05 2023
STATUS
approved
A099308 Numbers m whose k-th arithmetic derivative is zero for some k. Complement of A099309. +10
28
0, 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 17, 18, 19, 21, 22, 23, 25, 29, 30, 31, 33, 34, 37, 38, 41, 42, 43, 46, 47, 49, 53, 57, 58, 59, 61, 62, 65, 66, 67, 70, 71, 73, 77, 78, 79, 82, 83, 85, 89, 93, 94, 97, 98, 101, 103, 105, 107, 109, 113, 114, 118, 121, 126, 127, 129, 130 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
The first derivative of 0 and 1 is 0. The second derivative of a prime number is 0.
For all n, A003415(a(n)) is also a term of the sequence. A351255 gives the nonzero terms as ordered by their position in A276086. - Antti Karttunen, Feb 14 2022
REFERENCES
See A003415.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
Victor Ufnarovski and Bo Åhlander, How to Differentiate a Number, J. Integer Seqs., Vol. 6, 2003, #03.3.4.
FORMULA
For all n >= 0, A328309(a(n)) = n. - Antti Karttunen, Feb 14 2022
EXAMPLE
18 is on this list because the first through fifth derivatives are 21, 10, 7, 1, 0.
MATHEMATICA
dn[0]=0; dn[1]=0; dn[n_]:=Module[{f=Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus@@(n*f[[2]]/f[[1]])]]; d1=Table[dn[n], {n, 40000}]; nLim=200; lst={1}; i=1; While[i<=Length[lst], currN=lst[[i]]; pre=Intersection[Flatten[Position[d1, currN]], Range[nLim]]; pre=Complement[pre, lst]; lst=Join[lst, pre]; i++ ]; Union[lst]
PROG
(PARI)
\\ The following program would get stuck in nontrivial loops. However, we assume that the conjecture 3 in Ufnarovski & Åhlander paper holds ("The differential equation n^(k) = n has only trivial solutions p^p for primes p").
A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));
isA099308(n) = if(!n, 1, while(n>1, n = A003415checked(n)); (n)); \\ Antti Karttunen, Feb 14 2022
CROSSREFS
Cf. A003415 (arithmetic derivative of n), A099307 (least k such that the k-th arithmetic derivative of n is zero), A099309 (complement, numbers whose k-th arithmetic derivative is nonzero for all k), A351078 (first noncomposite reached when iterating the derivative from these numbers), A351079 (the largest term on such paths).
Cf. A328308, A328309 (characteristic function and their partial sums), A341999 (1 - charfun).
Cf. A276086, A328116, A351255 (permutation of nonzero terms), A351257, A351259, A351261, A351072 (number of prime(k)-smooth terms > 1).
Cf. also A256750 (number of iterations needed to reach either 0 or a number with a factor of the form p^p), A327969, A351088.
Union of A359544 and A359545.
KEYWORD
nonn
AUTHOR
T. D. Noe, Oct 12 2004
STATUS
approved
A359550 Multiplicative with a(p^e) = 1 if p > e, otherwise 0. +10
28
1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..100000
Index entries for characteristic functions.
FORMULA
Multiplicative with a(p^e) = [e < p], where [ ] is the Iverson bracket.
a(n) = [A129251(n) == 0] = [A327936(n) == 1] = [A342007(n) == 1].
a(n) = 1 - A342023(n).
Sum_{k=1..n} a(k) ~ c * n, where c = Product_{p prime} (1 - 1/p^p) = 0.7219902344... . - Amiram Eldar, Jan 07 2023
MATHEMATICA
f[p_, e_] := If[e < p, 1, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jan 06 2023 *)
PROG
(PARI) A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 2]<f[k, 1])); };
(Python)
from sympy import factorint
def A359550(n): return int(all(map(lambda d:d[0]>d[1], factorint(n).items()))) # Chai Wah Wu, Jan 06 2023
CROSSREFS
Characteristic function of A048103.
Cf. A129251, A327936, A328308, A342007, A342023 (one's complement), A359546, A359551 (Dirichlet inverse).
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Jan 06 2023
STATUS
approved
A099309 Numbers n whose k-th arithmetic derivative is nonzero for all k. Complement of A099308. +10
20
4, 8, 12, 15, 16, 20, 24, 26, 27, 28, 32, 35, 36, 39, 40, 44, 45, 48, 50, 51, 52, 54, 55, 56, 60, 63, 64, 68, 69, 72, 74, 75, 76, 80, 81, 84, 86, 87, 88, 90, 91, 92, 95, 96, 99, 100, 102, 104, 106, 108, 110, 111, 112, 115, 116, 117, 119, 120, 122, 123, 124, 125, 128, 132 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers of the form n = m*p^p (where p is prime), i.e., multiples of some term in A051674, have n' = (m + m')*p^p, which is again of the same form, but strictly larger iff m > 1. Therefore successive derivatives grow to infinity in this case, and they are constant when m = 1. There are other terms in this sequence, but I conjecture that they all eventually lead to a term of this form, e.g., 26 -> 15 -> 8 etc. - M. F. Hasler, Apr 09 2015
REFERENCES
See A003415.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
PROG
(PARI) is(n)=until(4>n=factorback(n~)*sum(i=1, #n, n[2, i]/n[1, i]), for(i=1, #n=factor(n)~, n[1, i]>n[2, i]||return(1))) \\ M. F. Hasler, Apr 09 2015
CROSSREFS
Cf. A003415 (arithmetic derivative of n), A099307 (least k such that the k-th arithmetic derivative of n is zero), A099308 (numbers whose k-th arithmetic derivative is zero for some k).
Cf. A341999 (characteristic function),
Positions of zeros in A256750, A351078, A351079 (after their initial zeros), also in A328308, A328312.
Subsequences include: A100716, A327929, A327934, A328251, A359547 (intersection with A048103).
KEYWORD
nonn
AUTHOR
T. D. Noe, Oct 12 2004
STATUS
approved
A341999 a(n) = 1 if the k-th arithmetic derivative is nonzero for all k >= 0, otherwise 0. +10
13
0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0
COMMENTS
Characteristic function of A099309.
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for characteristic functions
FORMULA
a(n) = 1 if n is in A100716 or ends there by repeated applications of A003415, otherwise a(n) = 0 (when n instead reaches 0 by such iteration).
For all n, a(n) >= A341996(n).
For all n > 0, a(A099309(n)) = a(A100716(n)) = 1.
For all n > 0, a(n) = [A256750(n) < 1].
For all n > 0, a(n) >= [A129251(n)>0], i.e., if A129251(n) is nonzero, then certainly a(n) = 1.
For all n > 1, a(n) >= [A341997(n) > 1].
a(n) = 1 - A328308(n), and for n >= 1, a(n) = A342023(n) + A359546(n). - Antti Karttunen, Jan 05 2023
PROG
(PARI)
A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));
A341999(n) = if(!n, n, while(n>1, n = A003415checked(n)); (!n));
CROSSREFS
Cf. A003415, A100716, A129251, A256750, A341996, A341997.
Cf. A099308 (positions of zeros), A099309 (of ones), A328308 (one's complement), A342023, A359542 (inverse Möbius transform), A359546.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 28 2021
STATUS
approved
A328307 a(n) tells how many numbers m there are in range 0..n such that the k-th arithmetic derivative of A276086(m) is zero for some k >= 0. +10
9
1, 2, 3, 4, 5, 6, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 11, 11, 12, 13, 13, 13, 13, 13, 13, 13, 14, 14, 15, 16, 17, 18, 18, 19, 19, 20, 21, 21, 22, 22, 22, 23, 23, 23, 24, 25, 25, 26, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 28, 29, 29, 29, 29, 30, 30, 31, 32, 32, 32, 33, 33, 34, 35, 35, 36, 36, 36, 37, 37, 37, 37, 37, 38 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n) = the number of such terms m in A328116 that m <= n.
Although in principle A276086 moves any n out of the "all hope lost" zone A100716 (where A328308 is always zero), back to its complement A048103, by comparing the ratio of this and A328309 it can be seen (see the Plot2-link in the Links-section) that such a transfer actually lessens the chances that by just iterating A003415 one could reach zero from there. Note also how the effect of the primorial base representation can be clearly seen in the folds and warps of that plot.
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..65537
Ratio of A328309(n)/A328307(n) plotted with OEIS Plot2-script
FORMULA
a(0) = 1; for n > 0, a(n) = a(n-1) + A328306(n).
For all n >= 0, a(A328116(n)) = n.
PROG
(PARI)
up_to = 65537;
A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));
A276086(n) = { my(i=0, m=1, pr=1, nextpr); while((n>0), i=i+1; nextpr = prime(i)*pr; if((n%nextpr), m*=(prime(i)^((n%nextpr)/pr)); n-=(n%nextpr)); pr=nextpr); m; };
A328308(n) = if(!n, 1, while(n>1, n = A003415checked(n)); (n));
A328306(n) = A328308(A276086(n));
A328307list(up_to) = { my(v=vector(up_to), s=A328306(0)); for(i=1, up_to, s += A328306(i); v[i] = s); (v); };
v328307 = A328307list(up_to);
A328307(n) = if(!n, 1, v328307[n]);
CROSSREFS
Partial sums of A328306, a left inverse of A328116.
Cf. A003415, A048103, A100716, A276086, A327969, A328306, A328308, A328309.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 12 2019
STATUS
approved
A368915 a(n) = 1 if there is no prime p such that p^p divides the arithmetic derivative of n, and 0 otherwise. +10
9
0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1
COMMENTS
Question: What is the asymptotic mean of this sequence (and its complement A341996)? Knowing the value for A360111 would solve this. See also related sequences like A354874 and A368916.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..100000
Index entries for characteristic functions
FORMULA
a(1) = 0; for n > 1, a(n) = A359550(A003415(n)).
For all n > 1, a(n) = 1 - A341996(n) = A359550(n) - A360111(n).
For all n > 1, A359550(n) >= a(n) >= A328308(n).
For all n >= 1, a(n) >= A354874(n).
a(n) = A368914(n) - A368913(n).
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 2]<f[k, 1])); };
A368915(n) = ((n>1)&&A359550(A003415(n)));
CROSSREFS
Characteristic function of A358215.
Cf. A003415, A328308, A341996 (one's complement), A354874, A359550, A360111, A368913, A368914, A368916 [= a(A276086(n))].
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 09 2024
STATUS
approved
A328306 a(n) = 1 if k-th arithmetic derivative of A276086(n) is zero for some k, otherwise 0. +10
7
1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0
COMMENTS
a(n) = 1 if A276086(n) is in A099308, 0 otherwise.
Question: Does the sequence have asymptotic mean? See also A328307 and A351071. - Antti Karttunen, Jan 10 2024
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for characteristic functions
Index entries for sequences related to primorial base
FORMULA
a(n) = A328308(A276086(n)).
For n > 0, a(n) <= A368916(n). - Antti Karttunen, Jan 10 2024
PROG
(PARI)
A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));
A276086(n) = { my(i=0, m=1, pr=1, nextpr); while((n>0), i=i+1; nextpr = prime(i)*pr; if((n%nextpr), m*=(prime(i)^((n%nextpr)/pr)); n-=(n%nextpr)); pr=nextpr); m; };
A328308(n) = if(!n, 1, while(n>1, n = A003415checked(n)); (n));
A328306(n) = A328308(A276086(n));
CROSSREFS
Characteristic function of A328116.
Cf. A003415, A099308, A276086, A328307 (partial sums), A328308, A351071, A368916.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 12 2019
STATUS
approved
A359546 a(n) = 1 if there is no factor of the form p^p in n, but for some k-th arithmetic derivative (k >= 1) of n such a factor exists; otherwise 0. +10
7
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1
COMMENTS
Question: What can be said about the distribution of 0's and 1's in this sequence? Compare also to A328308, A341996 and A359543.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..100000
Index entries for characteristic functions
FORMULA
a(n) = A341999(n) - A342023(n).
a(n) = A359550(n) * A341999(n).
a(n) = [A256750(n) < 0], where [ ] is the Iverson bracket.
EXAMPLE
a(15) = 1, because although 15 itself is not in A100716, its arithmetic derivative 15' = 8 is there.
a(26) = 1, as although neither 26 nor 26' = 15 are in A100716, the second derivative of 26, 26'' = 15' = 8 is there.
PROG
(PARI)
A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));
A327936(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = (f[k, 2]>=f[k, 1])); factorback(f); };
A341999(n) = if(!n, n, while(n>1, n = A003415checked(n)); (!n));
A359546(n) = ((1==A327936(n))&&A341999(n));
CROSSREFS
Characteristic function of A359547.
Cf. A003415, A048103, A256750, A327936, A328308, A341996, A341999, A342023, A359543, A359550.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 05 2023
STATUS
approved
A351071 Number of integers x in range A002110(n) .. A002110(1+n)-1 such that the k-th arithmetic derivative of A276086(x) is zero for some k, where A002110(n) is the n-th primorial. +10
6
1, 4, 8, 44, 216, 1474, 11130, 92489 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n) is the number of terms of A328116 in range A002110(n) .. A002110(1+n)-1.
a(n) is the number of terms in A351255 (and in A099308) whose largest prime factor (A006530) is A000040(1+n).
Ratio a(n) / A061720(n) develops as:
0: 1 / 1 = 1.0
1: 4 / 4 = 1.0
2: 8 / 24 = 0.333...
3: 44 / 180 = 0.244...
4: 216 / 2100 = 0.1029...
5: 1474 / 27720 = 0.05317...
6: 11130 / 480480 = 0.02316...
7: 92489 / 9189180 = 0.01006...
Computing term a(8) would need processing over 213393180 integers whose greatest prime factor is 23, from single A351255(105368) = 23 at start to product (2^1)*(3^2)*(5*4)*(7^6)*(11^10)*(13^12)*(17^16)*(19^18)*(23^22) at the end of the batch [number whose size in binary is 346 bits], and would required factoring integers of comparable size and more (see A351261), that might not all be easily factorable.
LINKS
Table of n, a(n) for n=0..7.
FORMULA
a(n) = Sum_{k=A002110(n) .. A002110(1+n)-1} A328306(k).
a(n) = A328307(A002110(1+n)) - A328307(A002110(n)).
EXAMPLE
There are eight terms [6, 7, 9, 12, 15, 20, 21, 28] that are >= A002110(2) and < A002110(3) in A328116 for which the corresponding terms [5, 10, 30, 25, 150, 375, 750, 5625] in A276086 (and A351255) are all in A099308, therefore a(2) = 8.
PROG
(PARI)
\\ Memoization would work quite badly here. (See comments in A351255. In practice sequence A328306 was computed first, up to its term a(9699690). Same data is available in A328116.)
A002110(n) = prod(i=1, n, prime(i));
A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));
A328308(n) = if(!n, 1, while(n>1, n = A003415checked(n)); (n));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A328306(n) = A328308(A276086(n));
A351071(n) = sum(k=A002110(n), A002110(1+n)-1, A328306(k));
CROSSREFS
Cf. A002110, A003415, A061720, A099308, A328306, A328307, A328308, A328116, A351067, A351069, A351255, A351261, A351072 (partial sums).
Cf. also A327969.
KEYWORD
nonn,hard,more
AUTHOR
Antti Karttunen, Feb 02 2022
STATUS
approved
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Last modified August 29 17:51 EDT 2024. Contains 375518 sequences. (Running on oeis4.)