A385540 Number of values of nonnegative s < n such that s^s == (-s)^s == s (mod n).

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

Offset

1,6

Links

Table of n, a(n) for n=1..100.

Mathematica

a[n_] := Count[Range[0, n-1], _?(PowerMod[#, #, n] == PowerMod[-#, #, n] == # &)]; Array[a, 100] (* Amiram Eldar, Jul 03 2025 *)

Prog

(Magma) [#[s: s in [0..n-1] | Modexp(s, s, n) eq s and Modexp(-s, s, n) eq s]: n in [1..100]];
(PARI) a(n) = sum(s=0, n-1, (s == Mod(s, n)^s) && (s == Mod(-s, n)^s)); \\ Michel Marcus, Jul 09 2025

Crossrefs

Cf. A065295, A384781, A385541.

Sequence in context: A328515 A356682 A323989 * A262988 A039999 A069842

Adjacent sequences: A385537 A385538 A385539 * A385541 A385542 A385543

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 02 2025

Status

approved