A386310 Number of divisors d of n such that 2*d^d == 0 (mod n).

1, 2, 1, 2, 1, 2, 1, 3, 2, 2, 1, 2, 1, 2, 1, 3, 1, 4, 1, 2, 1, 2, 1, 3, 2, 2, 3, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 2, 2, 2, 1, 4, 2, 4, 1, 2, 1, 6, 1, 3, 1, 2, 1, 2, 1, 2, 2, 5, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 2, 2, 1, 2, 1, 4, 3, 2, 1, 2, 1, 2, 1, 3, 1, 4, 1, 2, 1, 2, 1, 5, 1, 4, 2, 4

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 20 2025

Keywords

• nonn
• new

Crossrefs

Cf. A000005, A385429, A385662, A386930.

Programs

Magma

[1 + #[d: d in [1..n-1] | n mod d eq 0 and Modexp(d,d,n) eq -Modexp(d,d,n) mod n]: n in [1..100]];

Mathematica

Table[Length[Select[Divisors[n], PowerMod[#, #, n] == Mod[n - PowerMod[#, #, n], n] &]], {n, 1, 100}] (* Vaclav Kotesovec, Aug 23 2025 *)

PARI

a(n) = sumdiv(n, d, 2*Mod(d, n)^d == 0); \\ Michel Marcus, Aug 30 2025