A332655 a(n) = Sum_{k=1..n} (k/gcd(n, k))^n.

1, 2, 10, 84, 1301, 15693, 376762, 6168552, 176787631, 3770427352, 142364319626, 3152758480715, 154718778284149, 4340093860950619, 210971170836848270, 7281694486114555088, 435659030617933827137, 14181121059071691716406, 1052864393300587929716722, 41673907052879908244100770

Offset: 1

Author

Ilya Gutkovskiy, Feb 18 2020

Keywords

• nonn

Crossrefs

Cf. A031971, A057661, A226561, A332517, A332621, A332652, A332653, A332654.

Programs

Magma

[&+[(k div Gcd(n,k))^n:k in [1..n]]:n in [1..20]]; // Marius A. Burtea, Feb 18 2020

Mathematica

Table[Sum[(k/GCD[n, k])^n, {k, 1, n}], {n, 1, 20}]
Table[Sum[Sum[If[GCD[k, d] == 1, k^n, 0], {k, 1, d}], {d, Divisors[n]}], {n, 1, 20}]

Formula

a(n) = Sum_{k=1..n} (lcm(n, k)/n)^n.

a(n) = Sum_{d|n} Sum_{k=1..d, gcd(k, d) = 1} k^n.