|
|
A349162
|
|
a(n) = sigma(n) / gcd(sigma(n), A003961(n)), where A003961 shifts the prime factorization of n one step towards larger primes, and sigma is the sum of divisors function.
|
|
19
|
|
|
1, 1, 4, 7, 6, 4, 8, 5, 13, 6, 12, 28, 14, 8, 24, 31, 18, 13, 20, 2, 32, 12, 24, 4, 31, 14, 8, 56, 30, 24, 32, 7, 48, 18, 48, 91, 38, 20, 56, 10, 42, 32, 44, 28, 78, 24, 48, 124, 57, 31, 72, 98, 54, 8, 72, 40, 16, 30, 60, 8, 62, 32, 104, 127, 12, 48, 68, 14, 96, 48, 72, 13, 74, 38, 124, 140, 96, 56, 80, 62, 121, 42
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Small values are rare, but are not limited to the beginning. For example in range 1 .. 2^25, a(n) = 4 at n = 3, 6, 24, 792, 2720, 122944, 31307472.
Question: Would it be possible to prove that a(n) > 1 for all n > 2?
|
|
LINKS
|
|
|
FORMULA
|
|
|
MATHEMATICA
|
Array[#1/GCD[##] & @@ {DivisorSigma[1, #], If[# == 1, 1, Times @@ Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]]]} &, 82] (* Michael De Vlieger, Nov 11 2021 *)
|
|
PROG
|
(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
|
|
CROSSREFS
|
Cf. A000203, A003961, A028982 (positions of odd terms), A319630, A336702, A342671, A348992 (the odd part), A348993, A349161 (numerators), A349163, A349164, A349627, A349628, A350072 [= a(n^2)].
|
|
KEYWORD
|
nonn,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|