A328851 -id:A328851 - cp's OEIS frontend

A328853 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(k - 1).

1, 1, 2, 4, 4, 7, 6, 11, 11, 13, 10, 24, 12, 19, 22, 32, 16, 38, 18, 44, 32, 31, 22, 76, 34, 37, 46, 64, 28, 89, 30, 84, 52, 49, 58, 143, 36, 55, 62, 138, 40, 129, 42, 104, 116, 67, 46, 233, 69, 119, 82, 124, 52, 188, 94, 200, 92, 85, 58, 341, 60, 91, 168, 230

Offset: 1

Ilya Gutkovskiy, Oct 28 2019

nonn

Dirichlet convolution of A050367 with A114592.

Cf. A001055, A050367, A114592, A328851.

a(n) = Sum_{d|n} A050367(n/d) * A114592(d).

A328876 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(k + 1).

Original entry on oeis.org

1, 3, 4, 8, 6, 19, 8, 25, 16, 29, 12, 66, 14, 39, 40, 69, 18, 95, 20, 102, 54, 59, 24, 220, 41, 69, 72, 138, 30, 237, 32, 191, 82, 89, 84, 379, 38, 99, 96, 342, 42, 321, 44, 210, 206, 119, 48, 679, 78, 240, 124, 246, 54, 459, 128, 464, 138, 149, 60, 971

Offset: 1

Ilya Gutkovskiy, Oct 29 2019

nonn

Number of ways to factor n into distinct factors with 3 kinds of 2, 4 kinds of 3, ..., k+1 kinds of k.

Dirichlet convolution of A045778 with A050368.

Cf. A045778, A050368, A328851, A328877.

seq(n)={my(v=vector(n, k, k==1)); for(k=2, n, my(m=logint(n, k), p=(1 + x + O(x*x^m))^(k+1), w=vector(n)); for(i=0, m, w[k^i]=polcoef(p, i)); v=dirmul(v, w)); v} \\ Andrew Howroyd, Oct 29 2019

a(n) = Sum_{d|n} A045778(n/d) * A050368(d).

cp's OEIS Frontend

A328853 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(k - 1).

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