A387157 a(n) = A173557(sigma(n)), where A173557(n) is multiplicative with a(p^e) = p-1 and sigma is the sum of divisors function.

1, 2, 1, 6, 2, 2, 1, 8, 12, 2, 2, 6, 6, 2, 2, 30, 2, 24, 4, 12, 1, 2, 2, 8, 30, 12, 4, 6, 8, 2, 1, 12, 2, 2, 2, 72, 18, 8, 6, 8, 12, 2, 10, 12, 24, 2, 2, 30, 36, 60, 2, 6, 2, 8, 2, 8, 4, 8, 8, 12, 30, 2, 12, 126, 12, 2, 16, 12, 2, 2, 2, 96, 36, 36, 30, 24, 2, 12, 4, 60, 10, 12, 12, 6, 2, 20, 8, 8, 8, 24, 6, 12, 1, 2, 8

Offset: 1

Author

Antti Karttunen, Aug 19 2025

Keywords

• nonn
• new

Links

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

Crossrefs

Cf. A000203, A003958, A080398, A173557, A387158 (positions where equal to A173557(n)).

Cf. also A351442.

Programs

Mathematica

A387157[n_] := If[n == 1, 1, Times @@ (FactorInteger[DivisorSigma[1, n]][[All, 1]] - 1)];
Array[A387157, 100] (* Paolo Xausa, Aug 20 2025 *)

PARI

A387157(n) = factorback(apply(p -> p-1,factor(sigma(n))[,1]));

Formula

a(n) = A003958(A080398(n)).