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

1,4

Links

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

Formula

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

Mathematica

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

Prog

(Magma) [#[d: d in Divisors(n) | not IsPrime(2^d-1)]: n in [1..100]];
(PARI) a(n) = sumdiv(n, d, !isprime(2^d - 1)); \\ Michel Marcus, Jan 19 2025

Crossrefs

Cf. A000005, A000043, A379590.

Sequence in context: A153024 A066921 A076649 * A157235 A086289 A077807

Adjacent sequences: A380285 A380286 A380287 * A380289 A380290 A380291

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jan 18 2025

Status

approved