A345465 -id:A345465 - cp's OEIS frontend

A346196 a(n) = Sum_{d|n} (d!)^n.

1, 5, 217, 331793, 24883200001, 139314069504046721, 82606411253903523840000001, 6984964247141514123629140487675314433, 109110688415571316480344899355894085582848010077697, 395940866122425193243875570782668457763038823019173642240000001025

Offset: 1

Seiichi Manyama, Jul 10 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..30

Cf. A023887, A036739, A217576, A345465, A348146.

a[n_] := DivisorSum[n, (#!)^n &]; Array[a, 10] (* Amiram Eldar, Aug 30 2023 *)

PARI
```
a(n) = sumdiv(n, d, d!^n);
```

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

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

If p is prime, a(p) = 1 + (p!)^p.

A348146 a(n) = Sum_{d|n} (d!)^(n-d).

Original entry on oeis.org

1, 2, 2, 6, 2, 234, 2, 331842, 46658, 24883200258, 2, 139314179589392898, 2, 82606411253903523840004098, 619173642242176782338, 6984964247141514123665660725036072962, 2, 109110688415571335888754861121236891599318185050114, 2

Offset: 1

Wesley Ivan Hurt, Oct 02 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..61

Cf. A062363, A342628, A345465, A346196.

Table[Sum[(i!)^(n - i) (1 - Ceiling[n/i] + Floor[n/i]), {i, n}], {n, 20}]

a(n) = sumdiv(n, d, d!^(n-d)); \\ Seiichi Manyama, Oct 03 2021

my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(k!*x)^k))) \\ Seiichi Manyama, Oct 03 2021

a(p) = 2 for primes p.

G.f.: Sum_{k>=1} x^k/(1 - (k! * x)^k). - Seiichi Manyama, Oct 03 2021

A355669 a(n) = n! * Sum_{d|n} (d!)^(d - n/d).

Original entry on oeis.org

1, 6, 222, 331824, 24883200120, 139314069504005400, 82606411253903523840005040, 6984964247141514123629140377623274720, 109110688415571316480344899355894085582848000725760, 395940866122425193243875570782668457763038822400000006270570482400

Offset: 1

Seiichi Manyama, Aug 21 2022

nonn

Cf. A061095, A345465, A351165, A356662.

a[n_] := n! * DivisorSum[n, (#!)^(# - n/#) &]; Array[a, 10] (* Amiram Eldar, Aug 21 2022 *)

PARI
```
a(n) = n!*sumdiv(n, d, d!^(d-n/d));
```

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

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

cp's OEIS Frontend

A346196 a(n) = Sum_{d|n} (d!)^n.

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Mathematica

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A348146 a(n) = Sum_{d|n} (d!)^(n-d).

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

A355669 a(n) = n! * Sum_{d|n} (d!)^(d - n/d).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

PARI

Formula