A384834 Number of divisors of n such that (-d)^d == -d (mod n).

1, 2, 2, 2, 2, 4, 2, 2, 2, 3, 2, 3, 2, 3, 3, 2, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 2, 3, 2, 4, 2, 2, 3, 3, 2, 3, 2, 3, 3, 3, 2, 6, 2, 3, 3, 3, 2, 2, 2, 3, 3, 4, 2, 3, 3, 3, 3, 3, 2, 5, 2, 3, 3, 2, 4, 5, 2, 3, 3, 5, 2, 4, 2, 3, 3, 3, 2, 5, 2, 3, 2, 3, 2, 4, 3, 3, 3, 3, 2, 4, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3

Offset

1,2

Comments

a(n) >= 2 for n > 1, as d = 1 and n always work. a(n) = 2 if n is a prime power (A246655). - Robert Israel, Aug 26 2025

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

a:= n-> add(`if`(0=d+(-d)&^d mod n, 1, 0), d=numtheory[divisors](n)):
seq(a(n), n=1..100);  # Alois P. Heinz, Jul 26 2025

Mathematica

a[n_] := DivisorSum[n, 1 &, PowerMod[-#, #, n] == n-# &]; Array[a, 100] (* Amiram Eldar, Jul 24 2025 *)

Prog

(Magma) [1 + #[d: d in Divisors(n) | Modexp(-d, d, n) eq n-d mod n]: n in [1..100]];
(PARI) a(n) = sumdiv(n, d, Mod(-d, n)^d == n-d); \\ Michel Marcus, Jul 26 2025

Crossrefs

Cf. A000005, A386409.

Sequence in context: A227783 A216321 A058263 * A391684 A232398 A389781

Adjacent sequences: A384831 A384832 A384833 * A384835 A384836 A384837

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 23 2025

Status

approved