A332620 a(n) = Sum_{k=1..n} n^(n/gcd(n, k)).

1, 6, 57, 532, 12505, 93786, 4941265, 67117128, 2324524401, 40000400110, 2853116706121, 35664407810076, 3634501279107049, 66672041585829330, 3503151123049919265, 147573952606856413456, 13235844190181388226849, 236078448452969449231206, 35611553801885644604231641

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..385

Formula

a(n) = [x^n] Sum_{k>=1} Sum_{j>=1} phi(j) * n^j * x^(k*j).

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

a(n) = Sum_{d|n} phi(d) * n^d.

a(n) = n * A332621(n).

Mathematica

Table[Sum[n^(n/GCD[n, k]), {k, 1, n}], {n, 1, 19}]
Table[Sum[EulerPhi[d] n^d, {d, Divisors[n]}], {n, 1, 19}]
Table[SeriesCoefficient[Sum[Sum[EulerPhi[j] n^j x^(k j), {j, 1, n}], {k, 1, n}], {x, 0, n}], {n, 1, 19}]

Prog

(Magma) [&+[n^(n div Gcd(n, k)):k in [1..n]]:n in [1..20]]; // Marius A. Burtea, Feb 17 2020
(PARI) a(n) = sum(k=1, n, n^(n/gcd(n, k))); \\ Michel Marcus, Mar 10 2021

Crossrefs

Cf. A000010, A056665, A066108, A226561, A228640, A321349, A332621.

Sequence in context: A144070 A095900 A161434 * A371521 A246235 A213105

Adjacent sequences: A332617 A332618 A332619 * A332621 A332622 A332623

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 17 2020

Status

approved