[go: up one dir, main page]
login
The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
Search: a359236 -id:a359236
Displaying 1-9 of 9 results found.
page 1
     Sort: relevance | references | number | modified | created      Format: long | short | data
A359233
Number of divisors of 5*n-1 of form 5*k+1.
+10
11
1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 3, 2, 1, 1, 3, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 2, 2, 1, 3, 1, 3, 1, 1, 2, 4, 1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 1, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Also number of divisors of 5*n-1 of form 5*k+4.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A001876(5*n-1) = A001899(5*n-1).
G.f.: Sum_{k>0} x^k/(1 - x^(5*k-1)).
G.f.: Sum_{k>0} x^(4*k-3)/(1 - x^(5*k-4)).
MATHEMATICA
a[n_] := DivisorSum[5*n-1, 1 &, Mod[#, 5] == 1 &]; Array[a, 100] (* Amiram Eldar, Aug 23 2023 *)
PROG
(PARI) a(n) = sumdiv(5*n-1, d, d%5==1);
(PARI) a(n) = sumdiv(5*n-1, d, d%5==4);
(PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-x^(5*k-1))))
(PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^(4*k-3)/(1-x^(5*k-4))))
CROSSREFS
Cf. A078703, A099774, A359211.
Cf. A001876, A001899, A359236, A359237, A359238.
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 22 2022
STATUS
approved
A359237
Number of divisors of 5*n-3 of form 5*k+1.
+10
10
1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 2, 2, 1, 2, 1, 3, 1, 3, 1, 2, 1, 4, 1, 2, 2, 2, 1, 3, 1, 2, 1, 3, 2, 4, 1, 2, 1, 2, 2, 3, 1, 2, 1, 3, 1, 5, 1, 2, 1, 3, 1, 3, 2, 2, 2, 2, 1, 4, 1, 3, 1, 2, 1, 3, 1, 4, 3, 2, 1, 4, 1, 2, 1, 3, 1, 3, 2, 2, 1, 2, 2, 5, 1, 3, 1
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Also number of divisors of 5*n-3 of form 5*k+2.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A001876(5*n-3) = A001877(5*n-3).
G.f.: Sum_{k>0} x^k/(1 - x^(5*k-3)).
G.f.: Sum_{k>0} x^(2*k-1)/(1 - x^(5*k-4)).
MATHEMATICA
a[n_] := DivisorSum[5*n-3, 1 &, Mod[#, 5] == 1 &]; Array[a, 100] (* Amiram Eldar, Aug 23 2023 *)
PROG
(PARI) a(n) = sumdiv(5*n-3, d, d%5==1);
(PARI) a(n) = sumdiv(5*n-3, d, d%5==2);
(PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-x^(5*k-3))))
(PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^(2*k-1)/(1-x^(5*k-4))))
CROSSREFS
Cf. A001876, A001877, A359233, A359236, A359238.
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 22 2022
STATUS
approved
A359238
Number of divisors of 5*n-4 of form 5*k+1.
+10
7
1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 3, 4, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 3, 2, 2, 2, 4, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 2, 6, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 6, 2, 2, 2, 4, 2, 4, 2, 2, 3, 2
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A001876(5*n-4).
G.f.: Sum_{k>0} x^k/(1 - x^(5*k-4)).
MATHEMATICA
a[n_] := DivisorSum[5*n-4, 1 &, Mod[#, 5] == 1 &]; Array[a, 100] (* Amiram Eldar, Aug 23 2023 *)
PROG
(PARI) a(n) = sumdiv(5*n-4, d, d%5==1);
(PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-x^(5*k-4))))
CROSSREFS
Cf. A001876, A359233, A359236, A359237.
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 22 2022
STATUS
approved
A359269
Number of divisors of 5*n-2 of form 5*k+2.
+10
7
0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 1, 2, 0, 1, 0, 2, 0, 2, 0, 3, 0, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 4, 0, 1, 0, 2, 0, 2, 1, 2, 0, 1, 0, 3, 0, 3, 1, 2, 0, 1, 0, 2, 1, 1, 0, 4, 0, 1, 0, 4, 0, 1, 1, 2, 1, 1, 1, 3, 0, 1, 0, 2, 0, 4, 0, 2, 0, 1, 0, 4, 1, 2, 1, 2, 0, 1, 0, 4
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
Also number of divisors of 5*n-2 of form 5*k+4.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A001877(5*n-2) = A001899(5*n-2).
G.f.: Sum_{k>0} x^(2*k)/(1 - x^(5*k-1)).
G.f.: Sum_{k>0} x^(4*k-2)/(1 - x^(5*k-3)).
MATHEMATICA
a[n_] := DivisorSum[5*n-2, 1 &, Mod[#, 5] == 2 &]; Array[a, 100] (* Amiram Eldar, Aug 16 2023 *)
PROG
(PARI) a(n) = sumdiv(5*n-2, d, d%5==2);
(PARI) a(n) = sumdiv(5*n-2, d, d%5==4);
(PARI) my(N=100, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(2*k)/(1-x^(5*k-1)))))
(PARI) my(N=100, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(4*k-2)/(1-x^(5*k-3)))))
CROSSREFS
Cf. A001877, A001899, A359236.
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 23 2022
STATUS
approved
A359288
Number of divisors of 5*n-1 of form 5*k+3.
+10
4
0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 1, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 4, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 3, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, 0, 4, 0, 2, 4, 0, 0, 2, 0
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A001878(5*n-1).
G.f.: Sum_{k>0} x^(3*k-1)/(1 - x^(5*k-2)).
MATHEMATICA
a[n_] := DivisorSum[5*n-1, 1 &, Mod[#, 5] == 3 &]; Array[a, 100] (* Amiram Eldar, Aug 16 2023 *)
PROG
(PARI) a(n) = sumdiv(5*n-1, d, d%5==3);
(PARI) my(N=100, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(3*k-1)/(1-x^(5*k-2)))))
CROSSREFS
Cf. A001878.
Cf. A359233, A359287.
Cf. A359236, A359244, A359270.
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 24 2022
STATUS
approved
A363034
Sum of divisors of 5*n-2 of form 5*k+3.
+10
4
3, 8, 13, 21, 23, 28, 36, 38, 43, 59, 53, 58, 66, 68, 73, 94, 83, 96, 96, 98, 103, 129, 113, 118, 126, 136, 133, 164, 156, 148, 156, 158, 163, 207, 173, 178, 186, 188, 193, 252, 203, 229, 216, 218, 223, 269, 233, 238, 246, 256, 276, 304, 263, 268, 289, 278, 283, 365, 293, 298, 306, 336, 313, 374, 323
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Table of n, a(n) for n=1..65.
FORMULA
a(n) = A284281(5*n-2).
G.f.: Sum_{k>0} (5*k-2) * x^k / (1 - x^(5*k-2)).
MATHEMATICA
a[n_] := DivisorSum[5*n - 2, # &, Mod[#, 5] == 3 &]; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)
PROG
(PARI) a(n) = sumdiv(5*n-2, d, (d%5==3)*d);
CROSSREFS
Cf. A363033, A363035, A363053.
Cf. A284281, A359236, A363156.
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 06 2023
STATUS
approved
A364093
Sum of divisors of 5*n-2 of form 5*k+1.
+10
4
1, 1, 1, 7, 1, 1, 12, 1, 1, 23, 1, 1, 22, 1, 1, 33, 1, 12, 32, 1, 1, 43, 1, 1, 42, 17, 1, 53, 12, 1, 52, 1, 1, 84, 1, 1, 62, 1, 1, 84, 1, 43, 72, 1, 1, 83, 1, 1, 82, 32, 12, 93, 1, 1, 113, 1, 1, 155, 1, 1, 102, 12, 1, 113, 1, 42, 112, 27, 1, 123, 1, 1, 133, 63, 1, 154, 1, 1, 132, 1, 32, 194, 1, 12, 142
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
Table of n, a(n) for n=1..85.
FORMULA
a(n) = A284097(5*n-2).
G.f.: Sum_{k>0} (5*k-4) * x^(3*k-2) / (1 - x^(5*k-4)).
MATHEMATICA
a[n_] := DivisorSum[5*n - 2, # &, Mod[#, 5] == 1 &]; Array[a, 100] (* Amiram Eldar, Jul 17 2023 *)
PROG
(PARI) a(n) = sumdiv(5*n-2, d, (d%5==1)*d);
CROSSREFS
Cf. A364092, A364094, A364095.
Cf. A284097, A359236, A364097.
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 04 2023
STATUS
approved
A363156
Expansion of Sum_{k>0} k * x^k / (1 - x^(5*k-2)).
+10
1
1, 2, 3, 5, 5, 6, 8, 8, 9, 13, 11, 12, 14, 14, 15, 20, 17, 20, 20, 20, 21, 27, 23, 24, 26, 28, 27, 34, 32, 30, 32, 32, 33, 43, 35, 36, 38, 38, 39, 52, 41, 47, 44, 44, 45, 55, 47, 48, 50, 52, 56, 62, 53, 54, 59, 56, 57, 75, 59, 60, 62, 68, 63, 76, 65, 68, 68, 71, 69, 83, 71, 72, 81, 81, 75, 94, 77, 78, 80
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..79.
FORMULA
a(n) = (1/5) * Sum_{d | 5*n-2, d==3 (mod 5)} (d+2).
G.f.: Sum_{k>0} x^(3*k-2) / (1 - x^(5*k-4))^2.
MATHEMATICA
a[n_] := DivisorSum[5*n - 2, # + 2 &, Mod[#, 5] == 3 &]/5; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)
PROG
(PARI) a(n) = sumdiv(5*n-2, d, (d%5==3)*(d+2))/5;
CROSSREFS
Cf. A359236, A363034.
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 06 2023
STATUS
approved
A364097
Expansion of Sum_{k>0} k * x^(3*k-2) / (1 - x^(5*k-4)).
+10
1
1, 1, 1, 3, 1, 1, 4, 1, 1, 7, 1, 1, 6, 1, 1, 9, 1, 4, 8, 1, 1, 11, 1, 1, 10, 5, 1, 13, 4, 1, 12, 1, 1, 20, 1, 1, 14, 1, 1, 20, 1, 11, 16, 1, 1, 19, 1, 1, 18, 8, 4, 21, 1, 1, 25, 1, 1, 35, 1, 1, 22, 4, 1, 25, 1, 10, 24, 7, 1, 27, 1, 1, 29, 15, 1, 34, 1, 1, 28, 1, 8, 42, 1, 4, 30, 1, 1, 33, 1, 17, 32, 1, 1
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
Table of n, a(n) for n=1..93.
FORMULA
a(n) = (1/5) * Sum_{d | 5*n-2, d==1 (mod 5)} (d+4).
G.f.: Sum_{k>0} x^k / (1 - x^(5*k-2))^2.
MATHEMATICA
a[n_] := DivisorSum[5*n - 2, # + 4 &, Mod[#, 5] == 1 &]/5; Array[a, 100] (* Amiram Eldar, Jul 12 2023 *)
PROG
(PARI) a(n) = sumdiv(5*n-2, d, (d%5==1)*(d+4))/5;
CROSSREFS
Cf. A359236, A364093.
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 04 2023
STATUS
approved
page 1

Search completed in 0.008 seconds

Lookup Welcome Wiki Register Music Plot 2 Demos Index WebCam Contribute Format Style Sheet Transforms Superseeker Recents
The OEIS Community
Maintained by The OEIS Foundation Inc.
Last modified November 7 17:42 EST 2024. Contains 377536 sequences.
License Agreements, Terms of Use, Privacy Policy