A385103 Number of values of s, 0 < s < n, such that -(s^s) == s (mod n).

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

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 17 2025

Keywords

• nonn

Crossrefs

Cf. A065295, A151821, A373901, A382752, A384781, A384854.

Programs

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 20 2025

PARI

a(n) = sum(s=1, n-1, -Mod(s, n)^s == s); \\ Michel Marcus, Jun 19 2025