A385392 The number of divisors d of n such that -(d^d) == d (mod n).

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

Offset

1,2

Links

Table of n, a(n) for n=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 27 2025

Mathematica

a[n_] := DivisorSum[n, 1 &, PowerMod[#, #, n] == n-# &]; Array[a, 100] (* Amiram Eldar, Jun 27 2025 *)

Prog

(PARI) a(n) = sumdiv(n, d, -Mod(d, n)^d == d); \\ Michel Marcus, Jun 27 2025
(Magma) [1+#[d: d in [1..n-1] | n mod d eq 0 and Modexp(d, d, n) eq (n-d)]: n in [1..100]]; // Juri-Stepan Gerasimov, Jun 28 2025

Crossrefs

Cf. A032741, A065295, A384237, A384781, A384854, A385103.

Sequence in context: A263845 A385731 A079229 * A344972 A204988 A368332

Adjacent sequences: A385389 A385390 A385391 * A385393 A385394 A385395

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 27 2025

Status

approved