A358280 -id:A358280 - cp's OEIS frontend

A358279 a(n) = Sum_{d|n} (d-1)! * d^(n/d).

1, 3, 7, 29, 121, 747, 5041, 40433, 362935, 3629433, 39916801, 479006531, 6227020801, 87178326609, 1307674371487, 20922790212353, 355687428096001, 6402373709021811, 121645100408832001, 2432902008212950169, 51090942171709691335, 1124000727778046766849

Offset: 1

Seiichi Manyama, Nov 08 2022

Cf. A038507, A062363, A078308, A217576, A321521, A358280.

a[n_] := DivisorSum[n, (# - 1)! * #^(n/#) &]; Array[a, 22] (* Amiram Eldar, Aug 30 2023 *)

PARI
```
a(n) = sumdiv(n, d, (d-1)!*d^(n/d));
```

my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k!*x^k/(1-k*x^k)))

G.f.: Sum_{k>0} k! * x^k/(1 - k * x^k).

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

A358410 a(n) = Sum_{d|n} (d + n/d - 2)!/(d - 1)!.

Original entry on oeis.org

1, 2, 3, 9, 25, 130, 721, 5069, 40333, 363006, 3628801, 39917607, 479001601, 6227025848, 87178291591, 1307674408449, 20922789888001, 355687428461452, 6402373705728001, 121645100412461861, 2432902008176660217, 51090942171749356812, 1124000727777607680001

Offset: 1

Seiichi Manyama, Nov 14 2022

nonn

Cf. A157019, A358280, A358389.

a[n_] := DivisorSum[n, (# + n/# - 2)!/(# - 1)! &]; Array[a, 23] (* Amiram Eldar, Aug 30 2023 *)

a(n) = sumdiv(n, d, (d+n/d-2)!/(d-1)!);

my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, (k-1)!*(x/(1-x^k))^k))

G.f.: Sum_{k>0} (k-1)! * (x/(1 - x^k))^k.

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

cp's OEIS Frontend

A358279 a(n) = Sum_{d|n} (d-1)! * d^(n/d).

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A358410 a(n) = Sum_{d|n} (d + n/d - 2)!/(d - 1)!.

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Author

Keywords

Crossrefs

Programs

Mathematica

PARI

PARI

Formula