OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..386
FORMULA
a(n) = [x^n] Sum_{k>=1} Sum_{j>=1} phi(j) * n^(j-1) * x^(k*j).
a(n) = (1/n) * Sum_{k=1..n} n^(lcm(n, k)/k).
a(n) = (1/n) * Sum_{d|n} phi(d) * n^d.
a(n) = A332620(n) / n.
MATHEMATICA
Table[(1/n) Sum[n^(n/GCD[n, k]), {k, 1, n}], {n, 1, 19}]
Table[(1/n) Sum[EulerPhi[d] n^d, {d, Divisors[n]}], {n, 1, 19}]
Table[SeriesCoefficient[Sum[Sum[EulerPhi[j] n^(j - 1) x^(k j), {j, 1, n}], {k, 1, n}], {x, 0, n}], {n, 1, 19}]
PROG
(Magma) [(1/n)*&+[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)))/n; \\ Michel Marcus, Mar 10 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 17 2020
STATUS
approved