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

1,6

Comments

Number of divisors of n that belong to A000043.

Links

Table of n, a(n) for n=1..100.

Mathematica

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

Prog

(Magma) [#[d: d in Divisors(n) | IsPrime(2^d-1)]: n in [1..100]];
(PARI) a(n) = sumdiv(n, d, isprime(d) && ispseudoprime(2^d-1)); \\ Michel Marcus, Dec 28 2024

Crossrefs

Cf. A000005, A000043, A054723.

Sequence in context: A279126 A210679 A143262 * A035180 A163819 A301734

Adjacent sequences: A379587 A379588 A379589 * A379591 A379592 A379593

Keyword

nonn

Author

Juri-Stepan Gerasimov, Dec 26 2024

Status

approved