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A350109
a(n) = Sum_{k=1..n} k * floor(n/k)^n.
5
1, 6, 32, 295, 3201, 48321, 828323, 16910106, 388005909, 10019717653, 285409876785, 8920506515453, 302901435774351, 11113364096436947, 437903477186179875, 18447307498823123948, 827244767844150424228, 39346708569526147402819
OFFSET
1,2
LINKS
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
Main diagonal of A350106.
Sequence in context: A183681 A326985 A350485 * A185386 A368287 A276351
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 14 2021
STATUS
approved