A379590 a(n) is the number of prime divisors d of n such that 2^d - 1 is prime.

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 0, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 0, 2, 1, 2, 1, 2, 0, 3, 1, 1, 1, 2, 2, 2, 0, 2, 2, 2, 0, 3, 0, 1, 2, 1, 0, 2, 1, 2, 2, 2, 0, 2, 1, 2, 2, 1, 0, 3, 1, 2, 2, 1, 2, 2, 0, 2, 1, 3, 0, 2, 0, 1, 2, 2, 1, 3, 0, 2, 1, 1, 0, 3, 2, 1, 1, 1, 1, 3, 2, 1, 2, 1, 2, 2, 0, 2, 1, 2

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 26 2024

Keywords

• nonn

Comments

Number of divisors of n that belong to A000043.

Crossrefs

Cf. A000005, A000043, A054723.

Programs

Magma

[#[d: d in Divisors(n) | IsPrime(2^d-1)]: n in [1..100]];

Mathematica

a[n_] := DivisorSum[n, 1 &, PrimeQ[2^# - 1] &]; Array[a, 100] (* Amiram Eldar, Dec 27 2024 *)

PARI

a(n) = sumdiv(n, d, isprime(d) && ispseudoprime(2^d-1)); \\ Michel Marcus, Dec 28 2024