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

1,2

Links

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

Mathematica

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

Prog

(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]];

Crossrefs

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

Sequence in context: A118663 A205119 A355150 * A333915 A293234 A347441

Adjacent sequences: A385538 A385539 A385540 * A385542 A385543 A385544

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 02 2025

Status

approved