A345100 -id:A345100 - cp's OEIS frontend

A345098 a(n) = Sum_{k=1..n} floor(n/k)^floor(n/k).

1, 5, 29, 262, 3132, 46690, 823578, 16777484, 387420781, 10000003165, 285311673777, 8916100495209, 302875106639207, 11112006826381861, 437893890381686113, 18446744073726332260, 827240261886353544822, 39346408075296925042900

Offset: 1

Seiichi Manyama, Jun 07 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..386

Cf. A062796, A345094, A345100.

a[n_] := Sum[Floor[n/k]^Floor[n/k], {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Jun 08 2021 *)

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

my(N=20, x='x+O('x^N)); Vec(sum(j=1, N, (1-x^j)*sum(k=1, N, (k*x^j)^k))/(1-x))

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

a(n) ~ n^n. - Vaclav Kotesovec, Jun 11 2021

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

Original entry on oeis.org

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

Seiichi Manyama, Jun 10 2021

nonn

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

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

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

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

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))

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

cp's OEIS Frontend

A345098 a(n) = Sum_{k=1..n} floor(n/k)^floor(n/k).

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula