cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A328877 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(k - 1).

Original entry on oeis.org

1, 1, 2, 3, 4, 7, 6, 10, 9, 13, 10, 22, 12, 19, 22, 25, 16, 36, 18, 40, 32, 31, 22, 69, 30, 37, 42, 58, 28, 89, 30, 70, 52, 49, 58, 121, 36, 55, 62, 125, 40, 129, 42, 94, 108, 67, 46, 203, 63, 115, 82, 112, 52, 174, 94, 181, 92, 85, 58, 319, 60, 91, 156, 182
Offset: 1

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Author

Ilya Gutkovskiy, Oct 29 2019

Keywords

Comments

Number of ways to factor n into distinct factors with 1 kind of 2, 2 kinds of 3, ..., k-1 kinds of k.
Dirichlet convolution of A050368 with A316441.

Crossrefs

Programs

  • PARI
    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

Formula

a(n) = Sum_{d|n} A050368(n/d) * A316441(d).
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