A385541 Number of divisors of n such that d^d == (-d)^d == d (mod n).

1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 4, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 02 2025

Keywords

• nonn

Crossrefs

Cf. A000005, A384237, A384854, A385392, A385540.

Programs

Magma

[1 + #[d: d in [1..n-1] | n mod d eq 0 and Modexp(d,d,n) eq d and Modexp(-d,d,n) eq d]: n in [1..100]];

Mathematica

a[n_] := DivisorSum[n, 1 &, PowerMod[#, #, n] == PowerMod[-#, #, n] == Mod[#, n] &]; Array[a, 100] (* Amiram Eldar, Jul 03 2025 *)