A359731 -id:A359731 - cp's OEIS frontend

A359796 a(n) = Sum_{d|n} (2*d)^(d-1).

1, 5, 37, 517, 10001, 248873, 7529537, 268435973, 11019960613, 512000010005, 26559922791425, 1521681143418409, 95428956661682177, 6502111422505477189, 478296900000000010037, 37778931862957430145541, 3189059870763703892770817

Offset: 1

Seiichi Manyama, Jan 13 2023

Cf. A262843, A359731.

a[n_] := DivisorSum[n, (2*#)^(# - 1) &]; Array[a, 20] (* Amiram Eldar, Aug 14 2023 *)

PARI
```
a(n) = sumdiv(n, d, (2*d)^(d-1));
```

my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (2*k)^(k-1)*x^k/(1-x^k)))

G.f.: Sum_{k>0} (2 * k)^(k-1) * x^k / (1 - x^k).

A359732 a(n) = Sum_{d|n} d^(2*d-1).

Original entry on oeis.org

1, 9, 244, 16393, 1953126, 362797308, 96889010408, 35184372105225, 16677181699666813, 10000000000001953134, 7400249944258160101212, 6624737266949237373933820, 7056410014866816666030739694, 8819763977946281130541873428720

Offset: 1

Seiichi Manyama, Jan 12 2023

Cf. A308688, A308696, A359731.

a[n_] := DivisorSum[n, #^(2*# - 1) &]; Array[a, 15] (* Amiram Eldar, Aug 14 2023 *)

PARI
```
a(n) = sumdiv(n, d, d^(2*d-1));
```

my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(2*k-1)*x^k/(1-x^k)))

G.f.: Sum_{k>0} k^(2*k-1) * x^k / (1 - x^k).

cp's OEIS Frontend

A359796 a(n) = Sum_{d|n} (2*d)^(d-1).

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A359732 a(n) = Sum_{d|n} d^(2*d-1).

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Mathematica

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