A384854 The number of divisors d of n such that (-d)^d == d (mod n).

1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 5, 1, 1, 1, 2, 2, 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, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 10 2025

Keywords

• nonn
• changed

Links

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

Crossrefs

Cf. A000005, A032741, A065295, A384237, A384781.

Programs

Magma

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

Maple

a:= n-> add(`if`((-d)&^d-d mod n=0, 1, 0), d=numtheory[divisors](n)):
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 10 2025

PARI

a(n) = sumdiv(n, d, Mod(-d, n)^d == d); \\ Michel Marcus, Jun 11 2025

Formula

a(n) = 1 + number of proper divisors h of n such that (-h)^h = h (mod n).