A347415 a(n) = Sum_{k=1..n} floor((n/k)^k).

1, 3, 6, 11, 18, 31, 48, 76, 118, 184, 279, 426, 641, 966, 1448, 2163, 3228, 4805, 7137, 10586, 15681, 23198, 34278, 50606, 74632, 109987, 161954, 238312, 350432, 514999, 756407, 1110391, 1629219, 2389346, 3502578, 5132354, 7517523, 11007078, 16110784, 23573102, 34480937, 50420909

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..5000

Formula

a(n) ~ sqrt(2*Pi*n) * exp(exp(-1)*n - 1/2). - Vaclav Kotesovec, Sep 14 2021

Example

a(3) = [3/1] + [(3/2)^2] + [(3/3)^3] = 3 + 2 + 1 = 6.

Mathematica

a[n_] := Sum[Floor[(n/k)^k], {k, 1, n}]; Array[a, 40] (* Amiram Eldar, Aug 31 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, n^k\k^k);

Crossrefs

Cf. A006218, A062071, A153818, A344675, A345176, A347416.

Sequence in context: A123629 A212484 A279100 * A053992 A052825 A003082

Adjacent sequences: A347412 A347413 A347414 * A347416 A347417 A347418

Keyword

nonn

Author

Seiichi Manyama, Aug 31 2021

Status

approved