A347416 -id:A347416 - cp's OEIS frontend

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

Seiichi Manyama, Aug 31 2021

nonn

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

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

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

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

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

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

A350224 a(n) = Sum_{k=1..n} (-1)^(k+1) * floor((n/k)^n).

Original entry on oeis.org

1, 3, 25, 242, 3038, 45981, 817445, 16714015, 386682183, 9990395075, 285173906017, 8913939944658, 302838320218733, 11111330886027346, 437880557043106024, 18446463023081162520, 827233956902648749749, 39346258081658580861101

Offset: 1

Seiichi Manyama, Dec 20 2021

nonn

Cf. A344724, A347416, A350221, A350222, A350223.

a[n_] := Sum[(-1)^(k + 1)*Floor[(n/k)^n], {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Dec 20 2021 *)

a(n) = sum(k=1, n, (-1)^(k+1)*(n^n\k^n));

cp's OEIS Frontend

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

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