A342677 -id:A342677 - cp's OEIS frontend

A342675 a(n) = Sum_{d|n} d^(n-d+1).

1, 3, 4, 13, 6, 120, 8, 1161, 2197, 16148, 12, 603190, 14, 5773008, 50422464, 201359377, 18, 16590656229, 20, 269768284118, 4748723771432, 3138430473896, 24, 2972582195034162, 476837158203151, 3937376419253748, 1350852564961601560, 4066515044181860654, 30, 1036488835382356683530, 32

Offset: 1

Seiichi Manyama, Mar 18 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..599

Cf. A023887, A294645, A342628, A342677.

a[n_] := DivisorSum[n, #^(n - # + 1) &]; Array[a, 30] (* Amiram Eldar, Mar 18 2021 *)

PARI
```
a(n) = sumdiv(n, d, d^(n-d+1));
```

my(N=40, 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.

A359442 a(n) = Sum_{d|n} d^(n + 1 - d - n/d).

Original entry on oeis.org

1, 2, 2, 4, 2, 15, 2, 74, 83, 643, 2, 12635, 2, 117715, 397188, 2359426, 2, 103572204, 2, 1260918355, 13841818644, 25937425627, 2, 5612318393211, 152587890627, 23298085126579, 1853020231898564, 2422197090649523, 2, 1032944452284531101, 2, 10376297939508166658

Offset: 1

Seiichi Manyama, Jan 14 2023

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..605

Cf. A294645, A342628, A342629, A342677, A359700.

a[n_] := DivisorSum[n, #^(n + 1 - # - n/#) &]; Array[a, 32] (* Amiram Eldar, Aug 09 2023 *)

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

my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(k*x)^k/k)))

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

If p is prime, a(p) = 2.

cp's OEIS Frontend

A342675 a(n) = Sum_{d|n} d^(n-d+1).

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A359442 a(n) = Sum_{d|n} d^(n + 1 - d - n/d).

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula