A373898 Number of divisors d of n such that (n/d)^d == d (mod (n/d + d)).

1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 1

Offset

1,21

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Example

a(1) = 1 because the only divisor of 1 is 1 and (1/1)^1 (mod (1/1 + 1)) = 1;
a(6) = 1 because (6/1)^1 mod (6/1 + 1) = 6 (not equal to 1), (6/2)^2 mod (6/2 + 2) = 4 (not equal to 2), (6/3)^3  (mod (6/3 + 3) = 3 and (6/6)^6 mod (6/6 + 6) = 1 (not equal to 6), where 1, 2, 3 and 6 are divisors of 6.

Mathematica

a[n_]:=Sum[Boole[Mod[(n/d)^d, n/d+d]==d], {d, Divisors[n]}]; Array[a, 100] (* Stefano Spezia, Jun 22 2024 *)

Prog

(Magma) [#[d: d in Divisors(n) | (n div d)^d mod((n div d)+d) eq d]: n in [1..100]];
(PARI) a(n) = sumdiv(n, d, Mod(n/d, n/d + d)^d == d); \\ Michel Marcus, Jun 23 2024

Crossrefs

Cf. A000005.

Sequence in context: A370366 A342419 A226350 * A112609 A134363 A054015

Adjacent sequences: A373895 A373896 A373897 * A373899 A373900 A373901

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 22 2024

Status

approved