A387156 a(n) = A003557(sigma(n)), where A003557(n) is multiplicative with a(p^e) = p^(e-1), and sigma is the sum of divisors function.

1, 1, 2, 1, 1, 2, 4, 1, 1, 3, 2, 2, 1, 4, 4, 1, 3, 1, 2, 1, 16, 6, 4, 2, 1, 1, 4, 4, 1, 12, 16, 3, 8, 9, 8, 1, 1, 2, 4, 3, 1, 16, 2, 2, 1, 12, 8, 2, 1, 1, 12, 7, 9, 4, 12, 4, 8, 3, 2, 4, 1, 16, 4, 1, 2, 24, 2, 3, 16, 24, 12, 1, 1, 1, 2, 2, 16, 4, 8, 1, 11, 3, 2, 16, 18, 2, 4, 6, 3, 3, 8, 4, 64, 24, 4, 6, 7, 3, 2

Offset: 1

Author

Antti Karttunen, Aug 19 2025

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A003557, A062401, A080398, A387157.

Cf. also A386424, A386425.

Programs

Mathematica

A387156[n_] := # / Times @@ FactorInteger[#][[All, 1]] & [DivisorSigma[1, n]];
Array[A387156, 100] (* Paolo Xausa, Aug 20 2025 *)

PARI

A387156(n) = { my(s=sigma(n)); s/factorback(factor(s)[,1]); };

Formula

a(n) = A000203(n) / A080398(n).

a(n) = A062401(n) / A387157(n).