OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..386
FORMULA
a(n) = Sum_{k=1..n} k * Sum_{d|k} (d^n - (d - 1)^n)/d.
a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} (k^n - (k - 1)^n) * x^k/(1 - x^k)^2.
a(n) ~ n^n. - Vaclav Kotesovec, Dec 16 2021
MATHEMATICA
a[n_] := Sum[k * Floor[n/k]^n, {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Dec 14 2021 *)
PROG
(PARI) a(n) = sum(k=1, n, k*(n\k)^n);
(PARI) a(n) = sum(k=1, n, k*sumdiv(k, d, (d^n-(d-1)^n)/d));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 14 2021
STATUS
approved