A242649 -id:A242649 - cp's OEIS frontend

A242648 Dirichlet g.f.: Product_{n>=2} 1/(1-1/n^s)^sigma(n).

1, 3, 4, 13, 6, 24, 8, 46, 23, 36, 12, 116, 14, 48, 48, 161, 18, 156, 20, 174, 64, 72, 24, 484, 52, 84, 112, 232, 30, 360, 32, 526, 96, 108, 96, 841, 38, 120, 112, 726, 42, 480, 44, 348, 312, 144, 48, 1864, 93, 357, 144, 406, 54, 888, 144, 968, 160, 180

Offset: 1

N. J. A. Sloane, May 26 2014

nonn

Cf. A000203, A050367, A007896, A242649.

\\ Based on Michael Somos's code for A007896
n=101;
v = vector(n, k, k==1);
   for(k=2, n, m = #digits(n, k) - 1; A = (1 - x)^ -(sigma(k)) + x * O(x^m); w = vector(n); for(i=0, m, w[k^i] = polcoeff(A, i)); v = dirmul(v, w));
v

A328710 Dirichlet g.f.: (1/2) * Product_{i>=1, j>=1} (1 + (i*j)^(-s)).

Original entry on oeis.org

1, 2, 2, 4, 2, 8, 2, 10, 4, 8, 2, 22, 2, 8, 8, 19, 2, 22, 2, 22, 8, 8, 2, 56, 4, 8, 10, 22, 2, 40, 2, 38, 8, 8, 8, 71, 2, 8, 8, 56, 2, 40, 2, 22, 22, 8, 2, 128, 4, 22, 8, 22, 2, 56, 8, 56, 8, 8, 2, 132, 2, 8, 22, 73, 8, 40, 2, 22, 8, 40, 2, 202, 2, 8, 22, 22, 8, 40, 2, 128

Offset: 1

Ilya Gutkovskiy, Oct 26 2019

nonn

Cf. A000005, A050368, A242649, A328711.

Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^tau(k), where tau = A000005.

cp's OEIS Frontend

A242648 Dirichlet g.f.: Product_{n>=2} 1/(1-1/n^s)^sigma(n).

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A328710 Dirichlet g.f.: (1/2) * Product_{i>=1, j>=1} (1 + (i*j)^(-s)).

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Author

Keywords

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Formula