A356540 -id:A356540 - cp's OEIS frontend

A356539 a(n) = Sum_{d|n} d * 3^(n-d).

1, 5, 12, 49, 86, 492, 736, 3977, 8757, 34030, 59060, 384924, 531454, 2672528, 6672552, 26093113, 43046738, 261646137, 387420508, 2181624374, 4682526672, 17435870644, 31381059632, 204908769276, 299863458511, 1412168408630, 3392641222200, 13912336721584

Offset: 1

Seiichi Manyama, Aug 11 2022

nonn

Cf. A090879, A342675, A356540.

a[n_] := DivisorSum[n, # * 3^(n - #) &]; Array[a, 30] (* Amiram Eldar, Aug 11 2022 *)

PARI
```
a(n) = sumdiv(n, d, d*3^(n-d));
```

my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-(3*x)^k)))

G.f.: Sum_{k>=1} k * x^k/(1 - (3 * x)^k).

If p is prime, a(p) = p + 3^(p-1).

A356538 Expansion of e.g.f. Product_{k>0} 1/(1 - (2 * x)^k)^(1/2^k).

Original entry on oeis.org

1, 1, 5, 27, 249, 2085, 30645, 354375, 6542865, 108554985, 2330525925, 45331607475, 1288779532425, 28889867731725, 876160258298325, 25315531795929375, 860642393272286625, 26527678331237708625, 1063065483349950205125, 36393649136002135852875

Offset: 0

Seiichi Manyama, Aug 11 2022

nonn

Cf. A000041, A006950, A356530, A356540.

Cf. A090879.

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

a090879(n) = sumdiv(n, d, d*2^(n-d));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, i, a090879(j)*v[i-j+1]/(i-j)!)); v;

a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} A090879(k) * a(n-k)/(n-k)!.

cp's OEIS Frontend

A356539 a(n) = Sum_{d|n} d * 3^(n-d).

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A356538 Expansion of e.g.f. Product_{k>0} 1/(1 - (2 * x)^k)^(1/2^k).

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Author

Keywords

Crossrefs

Programs

PARI

PARI

Formula