A332652 a(n) = Sum_{k=1..n} n^(k/gcd(n, k)).

1, 4, 15, 76, 785, 7836, 137263, 2130976, 47895489, 1010012140, 28531167071, 743044702104, 25239592216033, 797785008119932, 31147773583464735, 1157442765678719056, 51702516367896047777, 2185932446984222457444, 109912203092239643840239, 5255987282125826560192520

Offset: 1

Author

Ilya Gutkovskiy, Feb 18 2020

Keywords

• nonn

Crossrefs

Cf. A031972, A056665, A057661, A226561, A228640, A332620, A332621, A332653, A332655.

Programs

Magma

[&+[n^(k div Gcd(n,k)):k in [1..n]]:n in [1..21]]; // Marius A. Burtea, Feb 18 2020

Mathematica

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

Formula

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

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

a(n) = n * A332653(n).