A386930 Number of divisors d of n such that (-d)^d == -d^d (mod n).

1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 4, 4, 2, 5, 2, 4, 4, 3, 2, 5, 3, 3, 4, 4, 2, 5, 2, 5, 4, 3, 4, 7, 2, 3, 4, 5, 2, 5, 2, 4, 6, 3, 2, 6, 3, 5, 4, 4, 2, 7, 4, 5, 4, 3, 2, 6, 2, 3, 6, 6, 4, 5, 2, 4, 4, 5, 2, 9, 2, 3, 6, 4, 4, 5, 2, 6, 5, 3, 2, 6, 4, 3, 4, 5, 2, 8, 4, 4, 4, 3, 4, 7, 2, 5, 6, 7

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 08 2025

Keywords

• nonn
• changed

Crossrefs

Cf. A000005, A384237, A384834, A384854, A385392, A385638.

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

a[n_] := DivisorSum[n, 1 &, PowerMod[-#, #, n] == Mod[-PowerMod[#, #, n], n] &]; Array[a, 100] (* Amiram Eldar, Aug 09 2025 *)

PARI

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