A387400 Number of nonnegative s < n such that s^s == s^n (mod n).

1, 1, 1, 2, 1, 4, 2, 3, 3, 5, 1, 7, 2, 6, 8, 7, 3, 8, 2, 9, 7, 5, 2, 12, 5, 6, 9, 11, 2, 15, 3, 15, 8, 7, 9, 13, 2, 8, 8, 17, 5, 18, 3, 11, 14, 7, 2, 24, 9, 13, 10, 14, 1, 20, 11, 17, 9, 8, 1, 27, 4, 9, 19, 31, 15, 18, 3, 12, 10, 22, 2, 23, 5, 9, 17, 13, 16, 23, 4, 33, 26, 10, 1, 31, 13, 9, 12, 20, 4, 27

Offset

1,4

Links

James C. McMahon, Table of n, a(n) for n = 1..1000

Mathematica

a[n_]:=Length[Select[Range[n]-1, PowerMod[#, #, n]==PowerMod[#, n, n]&]]; Array[a, 90] (* James C. McMahon, Sep 05 2025 *)

Prog

(Magma) [#[s: s in [0..n-1] | Modexp(s, s, n) eq Modexp(s, n, n)]: n in [1..90]];
(PARI) a(n) = sum(s=0, n-1, Mod(s, n)^n == Mod(s, n)^s); \\ Michel Marcus, Aug 30 2025

Crossrefs

Cf. A065295, A182816.

Sequence in context: A135941 A036998 A121464 * A090278 A256143 A352791

Adjacent sequences: A387397 A387398 A387399 * A387401 A387402 A387403

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 28 2025

Status

approved