A384781 Number of values of s, 0 < s <= n - 1, such that (-s)^s == s (mod n).

0, 1, 0, 0, 1, 2, 1, 0, 1, 4, 0, 1, 1, 3, 3, 0, 0, 4, 0, 1, 2, 3, 1, 1, 3, 6, 1, 3, 1, 6, 1, 0, 3, 2, 2, 3, 3, 3, 2, 1, 1, 6, 0, 3, 5, 3, 1, 1, 3, 8, 2, 2, 2, 4, 3, 2, 1, 5, 0, 3, 3, 3, 7, 0, 5, 6, 0, 1, 3, 8, 1, 3, 3, 8, 5, 3, 4, 6, 1, 1, 4, 3, 0, 5, 2, 4, 6, 2, 4, 10, 5, 2, 3, 3, 2, 1, 4, 8, 5, 5

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 09 2025

Keywords

• nonn

Crossrefs

Cf. A065295, A151821, A373901 (k such that a(k) = 0), A382752, A384854.

Programs

Magma

[#[s: s in [1..n-1] | Modexp((-s),s,n) eq s]: n in [1..100]];

Maple

a:= n-> add(`if`((-s)&^s-s mod n=0, 1, 0), s=1..n-1):
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 09 2025

Mathematica

a[n_]:=Length[Select[Range[n-1],PowerMod[-#,#,n]==# &]]; Array[a,100] (* Stefano Spezia, Jun 11 2025 *)

PARI

a(n) = sum(s=1, n-1, Mod(-s, n)^s == s); \\ Michel Marcus, Jun 11 2025