A345176 a(n) = Sum_{k=1..n} floor(n/k)^k.

1, 3, 5, 10, 12, 26, 28, 52, 73, 115, 117, 295, 297, 439, 713, 1160, 1162, 2448, 2450, 4644, 6832, 8902, 8904, 23536, 25639, 33857, 53247, 84961, 84963, 192237, 192239, 318477, 493909, 625015, 695789, 1761668, 1761670, 2285996, 3872598, 6255230, 6255232, 13392362

Offset

1,2

Links

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

Formula

G.f.: (1/(1 - x)) * Sum_{j>=1} Sum_{k>=1} (k*x^k)^j * (1 - x^j).

a(n) ~ 3^((n - mod(n,3))/3 + 1)/2. - Vaclav Kotesovec, Jun 11 2021

Mathematica

a[n_] := Sum[Floor[n/k]^k, {k, 1, n}]; Array[a, 40] (* Amiram Eldar, Jun 10 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, (n\k)^k);
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(j=1, N, (1-x^j)*sum(k=1, N, (k*x^k)^j))/(1-x))

Crossrefs

Cf. A001923, A006218, A332469, A345098, A345100.

Sequence in context: A266663 A007557 A034746 * A275219 A080931 A299533

Adjacent sequences: A345173 A345174 A345175 * A345177 A345178 A345179

Keyword

nonn

Author

Seiichi Manyama, Jun 10 2021

Status

approved