login
A373898
Number of divisors d of n such that (n/d)^d == d (mod (n/d + d)).
2
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved