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A332624
a(n) = Sum_{k=1..n} ceiling(n/k)^n.
1
1, 5, 36, 289, 3433, 47578, 842499, 16850338, 389415029, 10010878371, 285679026506, 8918295095267, 302973286652448, 11112691430262573, 437929106387544254, 18447028378472722051, 827256956775203666857, 39346558275376372606086, 1978429667078835508142129
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