Voozh

A386409

Number of nonnegative values s < n such that (-s)^s == -s (mod n).

1, 1, 2, 2, 2, 4, 2, 4, 3, 4, 3, 7, 5, 5, 6, 6, 4, 6, 4, 9, 8, 5, 2, 13, 4, 8, 3, 9, 4, 14, 3, 6, 7, 8, 12, 11, 3, 7, 10, 17, 5, 16, 6, 9, 10, 5, 2, 19, 7, 8, 10, 13, 3, 6, 11, 18, 11, 7, 3, 27, 5, 7, 14, 10, 16, 17, 5, 13, 7, 21, 4, 21, 5, 6, 14, 12, 12, 21, 5, 27, 6, 11, 3, 29, 16, 10, 9, 19, 4, 23

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..90.

MATHEMATICA

a[n_] := Count[Range[0, n-1], _?(PowerMod[-#, #, n] == n - # &)]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Jul 21 2025 *)

PROG

(Magma) [#[s: s in [0..n-1] | Modexp(-s, s, n) eq n-s mod n]: n in [1..90]];

(PARI) a(n) = sum(s=0, n-1, Mod(-s, n) == Mod(-s, n)^s); \\ Michel Marcus, Aug 22 2025

CROSSREFS

Cf. A065295, A384781, A385103, A385540, A385729.