OFFSET
1,2
FORMULA
a(n) = [x^n] x/(1 - x)^2 + (x/(1 - x)) * Sum_{k>=1} ((k + 1)^n - k^n) * x^k / (1 - x^k).
a(n) = n + Sum_{k=1..n-1} Sum_{d|k} ((d + 1)^n - d^n).
MATHEMATICA
Table[Sum[Ceiling[n/k]^n, {k, 1, n}], {n, 1, 19}]
Table[n + Sum[Sum[(d + 1)^n - d^n, {d, Divisors[k]}], {k, 1, n - 1}], {n, 1, 19}]
Table[SeriesCoefficient[x/(1 - x)^2 + x/(1 - x) Sum[((k + 1)^n - k^n) x^k/(1 - x^k), {k, 1, n}], {x, 0, n}], {n, 1, 19}]
PROG
(Magma) [&+[Ceiling(n/k)^n:k in [1..n]]:n in [1..20]]; // Marius A. Burtea, Feb 17 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 17 2020
STATUS
approved