A343514 a(n) = Sum_{k=1..n} (k/gcd(n, k))^4.

1, 2, 18, 84, 355, 645, 2276, 3192, 7413, 9400, 25334, 18395, 60711, 52747, 88760, 106688, 243849, 137790, 432346, 275570, 499867, 522513, 1151404, 561415, 1542125, 1214436, 1907502, 1569673, 3756719, 1344999, 5274000, 3451216, 4970577, 4690778, 7499154, 4217504, 12948595, 8207261, 11565572

Offset

1,2

Links

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

Formula

a(n) = Sum_{d|n} A053820(d).

If n is prime, a(n) = n*(n - 1)*(2*n - 1)*(3*n^2 - 3*n - 1)/30 + 1. - Robert Israel, Nov 18 2025

Maple

f:= proc(n) local k; add((k/igcd(n, k))^4, k=1..n) end proc:
map(f, [$1..50]); # Robert Israel, Nov 18 2025

Mathematica

Table[Sum[(k/GCD[n, k])^4, {k, 1, n}], {n, 1, 39}]

Prog

(PARI) a(n) = sum(k=1, n, (k/gcd(n, k))^4); \\ Michel Marcus, Apr 17 2021

Crossrefs

Cf. A053820, A057661, A332654, A343498, A343513.

Sequence in context: A176496 A091940 A068605 * A387969 A360301 A070171

Adjacent sequences: A343511 A343512 A343513 * A343515 A343516 A343517

Keyword

nonn,look

Author

Ilya Gutkovskiy, Apr 17 2021

Status

approved