A332624 a(n) = Sum_{k=1..n} ceiling(n/k)^n.

1, 5, 36, 289, 3433, 47578, 842499, 16850338, 389415029, 10010878371, 285679026506, 8918295095267, 302973286652448, 11112691430262573, 437929106387544254, 18447028378472722051, 827256956775203666857, 39346558275376372606086, 1978429667078835508142129

Offset

1,2

Links

Table of n, a(n) for n=1..19.

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

Cf. A006590, A031971, A332469, A332490, A332623.

Sequence in context: A188899 A052203 A371775 * A027331 A357153 A255489

Adjacent sequences: A332621 A332622 A332623 * A332625 A332626 A332627

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 17 2020

Status

approved