A367510 -id:A367510 - cp's OEIS frontend

A367509 a(n) = Sum_{d|n} (2*d+1)^n.

3, 34, 370, 7267, 161294, 4960812, 170861562, 7019201348, 322728071069, 16705828227476, 952809758091074, 59628239376008854, 4052555153020570590, 297587425607933152700, 23465266173840431204452, 1978033864507607364591749, 177482997121587371955312038

Offset: 1

Seiichi Manyama, Nov 21 2023

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..351

Cf. A163190, A367510.

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

a(n) = Sum_{k=0..n} 2^k * binomial(n,k) * sigma_k(n).

A367506 a(n) = Sum_{d|n} (d+n)^n.

Original entry on oeis.org

2, 25, 280, 6017, 107776, 3897218, 107510656, 4867995713, 204519070720, 10904505179450, 585061309782016, 38168392129581810, 2481946587976990720, 185404290282527361386, 14389574562121084305408, 1221867855128546542385409, 108430221517525671050739712

Offset: 1

Seiichi Manyama, Nov 21 2023

nonn

Cf. A163190, A163191, A367493, A367507, A367510.

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

a(n) = Sum_{k=0..n} n^(n-k) * binomial(n,k) * sigma_k(n).

cp's OEIS Frontend

A367509 a(n) = Sum_{d|n} (2*d+1)^n.

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