A374152 Number of divisors d of n such that d^(n/d) == d (mod (d + n/d)).

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

Offset

1,2

Comments

For all n, the divisors counted in a(n) include 1 and n.

Links

Table of n, a(n) for n=1..90.

Example

a(8) = 3 because the divisors of 8 are 1, 2, 4 and 8, and
  1^(8/1) == 1 (mod (1 + 8/1)),
  4^(8/4) == 4 (mod (4 + 8/4)) and
  8^(8/8) == 8 (mod (8 + 8/8)), but
  2^(8/2) != 2 (mod (2 + 8/2)).

Mathematica

a[n_]:=Sum[Boole[Mod[d^(n/d), n/d+d]==d], {d, Divisors[n]}]; Array[a, 90] (* Stefano Spezia, Jun 30 2024 *)

Prog

(Magma) [#[d: d in Divisors(n) | d^(n div d) mod ((n div d)+d) eq d]: n in [1..90]]

Crossrefs

Cf. A000005, A373898.

Sequence in context: A332025 A212300 A165074 * A273165 A336313 A095139

Adjacent sequences: A374149 A374150 A374151 * A374153 A374154 A374155

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 29 2024

Status

approved