A356436 -id:A356436 - cp's OEIS frontend

A356437 a(n) = n! * Sum_{k=1..n} sigma_k(k)/k.

1, 7, 77, 1946, 84754, 6202524, 636369348, 89979720144, 16431405256656, 3796658174518560, 1077102230236529760, 368915006390671969920, 149873555740938949215360, 71297150722148582901815040, 39244301012876892023553235200

Offset: 1

Seiichi Manyama, Aug 07 2022

nonn

Cf. A023887, A356297, A356436, A356440.

Table[n! * Sum[DivisorSigma[k, k]/k, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Aug 07 2022 *)

PARI
```
a(n) = n!*sum(k=1, n, sigma(k, k)/k);
```

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

E.g.f.: -(1/(1-x)) * Sum_{k>0} log(1 - (k*x)^k)/k.

a(n) ~ n! * n^(n-1). - Vaclav Kotesovec, Aug 07 2022

A356439 Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k)^(1/k) )^(1/(1-x)).

Original entry on oeis.org

1, 1, 6, 39, 344, 3410, 42234, 567126, 8812880, 149409144, 2793232440, 56224856160, 1234342760232, 28773852409848, 718719835537872, 19045601930731320, 534564416062012800, 15792205306586537280, 491639547448322794944, 16024048206145815040704

Offset: 0

Seiichi Manyama, Aug 07 2022

nonn

Cf. A353993, A356436, A356440.

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

a356436(n) = n!*sum(k=1, n, sumdiv(k, d, d^(k/d))/k);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356436(j)*binomial(i-1, j-1)*v[i-j+1])); v;

a(0) = 1; a(n) = Sum_{k=1..n} A356436(k) * binomial(n-1,k-1) * a(n-k).

cp's OEIS Frontend

A356437 a(n) = n! * Sum_{k=1..n} sigma_k(k)/k.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

A356439 Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k)^(1/k) )^(1/(1-x)).

Views

Author

Keywords

Crossrefs

Programs

PARI

PARI

Formula