A380288 a(n) is the number of divisors d of n such that 2^d - 1 is not prime.

1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 2, 4, 1, 2, 2, 4, 1, 4, 1, 4, 2, 3, 2, 6, 2, 2, 3, 4, 2, 5, 1, 5, 3, 2, 2, 7, 2, 2, 2, 6, 2, 5, 2, 5, 4, 3, 2, 8, 2, 4, 2, 4, 2, 6, 3, 6, 2, 3, 2, 9, 1, 2, 4, 6, 2, 6, 2, 4, 3, 5, 2, 10, 2, 3, 4, 4, 3, 5, 2, 8, 4, 3, 2, 9, 2, 3, 3, 7, 1, 9, 2, 5, 2, 3, 2, 10, 2, 4, 5, 7

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 18 2025

Keywords

• nonn

Crossrefs

Cf. A000005, A000043, A379590.

Programs

Magma

[#[d: d in Divisors(n) | not IsPrime(2^d-1)]: n in [1..100]];

Mathematica

a[n_] := DivisorSum[n, 1 &, !PrimeQ[2^# - 1] &]; Array[a, 100] (* Amiram Eldar, Jan 19 2025 *)

PARI

a(n) = sumdiv(n, d, !isprime(2^d - 1)); \\ Michel Marcus, Jan 19 2025

Formula

a(n) = A000005(n) - A379590(n).