A388258 - OEIS

A388258

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

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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..85.

MATHEMATICA

a[n_] := DivisorSum[n, 1 &, PowerMod[#, #, n] == Mod[-PowerMod[-#, n, n], n] &]; Array[a, 100] (* Amiram Eldar, Sep 20 2025 *)

PROG

(Magma) [1 + #[d: d in [1..n-1] | n mod d eq 0 and Modexp(d, d, n) eq -Modexp(-d, n, n) mod n]: n in [1..85]];

(PARI) a(n) = sumdiv(n, d, Mod(d, n)^d == - Mod(-d, n)^n); \\ Michel Marcus, Sep 16 2025

CROSSREFS

Cf. A000005, A386776, A387857.