A336457 a(n) = A065330(sigma(n)), where A065330 is fully multiplicative with a(2) = a(3) = 1, and a(p) = p for primes p > 3.

1, 1, 1, 7, 1, 1, 1, 5, 13, 1, 1, 7, 7, 1, 1, 31, 1, 13, 5, 7, 1, 1, 1, 5, 31, 7, 5, 7, 5, 1, 1, 7, 1, 1, 1, 91, 19, 5, 7, 5, 7, 1, 11, 7, 13, 1, 1, 31, 19, 31, 1, 49, 1, 5, 1, 5, 5, 5, 5, 7, 31, 1, 13, 127, 7, 1, 17, 7, 1, 1, 1, 65, 37, 19, 31, 35, 1, 7, 5, 31, 121, 7, 7, 7, 1, 11, 5, 5, 5, 13, 7, 7, 1, 1, 5, 7, 49

Offset: 1

Author

Antti Karttunen, Jul 24 2020

Keywords

• nonn
• mult

Comments

Sequence removes prime factors 2 and 3 from the prime factorization of the sum of divisors of n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A038502, A065330, A161942, A336458.

Cf. also A336455.

Programs

Mathematica

Array[Times @@ Map[#1^#2 & @@ # &, DeleteCases[FactorInteger[DivisorSigma[1, #]], ?(First@ # <= 3 &)]] &, 97] (* _Michael De Vlieger, Jul 24 2020 *)

PARI

A065330(n) = (n>>valuation(n, 2)/3^valuation(n, 3));
A336457(n) = A065330(sigma(n));

Formula

a(n) = A065330(A000203(n)) = A038502(A161942(n)).

Multiplicative with a(p^e) = A065330(1 + p + p^2 + ... + p^e).