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

1,2

Links

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A385429, A385662, A386930.

Sequence in context: A023120 A167970 A126433 * A237271 A336041 A176725

Adjacent sequences: A386307 A386308 A386309 * A386311 A386312 A386313

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 20 2025

Status

approved