A359053 -id:A359053 - cp's OEIS frontend

A359052 a(n) = Sum_{d|n} sigma_d(d)^n.

1, 26, 21953, 5554572467, 298500366308609377, 11413459460309090641106905930, 256925761343390078522337875137209684721665, 6476754651706496208416137876625690606583079440495100502628

Offset: 1

Seiichi Manyama, Dec 14 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..26

Cf. A344060, A359053, A359054.

a[n_] := DivisorSum[n, DivisorSigma[#, #]^n &]; Array[a, 8] (* Amiram Eldar, Aug 27 2023 *)

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

my(N=10, x='x+O('x^N)); Vec(sum(k=1, N, (sigma(k, k)*x)^k/(1-(sigma(k, k)*x)^k)))

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

A359054 a(n) = Sum_{d|n} sigma_d(d)^d.

Original entry on oeis.org

1, 26, 21953, 5554571867, 298500366308609377, 11413459460309090640625021978, 256925761343390078522337875137209684721665, 6476754651706496208416137876625690606552226172163824554588

Offset: 1

Seiichi Manyama, Dec 14 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..26

Cf. A344047, A359052, A359053.

a[n_] := DivisorSum[n, DivisorSigma[#, #]^# &]; Array[a, 8] (* Amiram Eldar, Aug 27 2023 *)

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

my(N=10, x='x+O('x^N)); Vec(sum(k=1, N, (sigma(k, k)*x)^k/(1-x^k)))

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

cp's OEIS Frontend

A359052 a(n) = Sum_{d|n} sigma_d(d)^n.

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A359054 a(n) = Sum_{d|n} sigma_d(d)^d.

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula