A385731 Number of divisors d of n such that (-d) == (-d)^d == d^d (mod n).

1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 08 2025

Keywords

• nonn

Crossrefs

Cf. A000005, A384237, A384854, A385392, A385540, A385729.

Programs

Magma

[#[d: d in Divisors(n) | Modexp(d, d, n) eq n-d and Modexp(-d, d, n) eq n-d]: n in [1..100]];

Mathematica

a[n_]:=Length[Select[Divisors[n],Mod[-#,n]==PowerMod[-#,#,n]==PowerMod[#,#,n]&]];Array[a,100] (* James C. McMahon, Jul 21 2025 *)

PARI

a(n) = sumdiv(n, d, (-d == Mod(d, n)^d) && (-d == Mod(-d, n)^d)); \\ Michel Marcus, Jul 09 2025