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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A383791 Numerators of the sequence whose Dirichlet convolution with itself yields fourth powers (A000583).

Original entry on oeis.org

1, 8, 81, 96, 625, 324, 2401, 1280, 19683, 2500, 14641, 3888, 28561, 9604, 50625, 17920, 83521, 19683, 130321, 30000, 194481, 58564, 279841, 51840, 1171875, 114244, 2657205, 115248, 707281, 101250, 923521, 258048, 1185921, 334084, 1500625, 236196, 1874161, 521284, 2313441
Offset: 1

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Author

Vaclav Kotesovec, May 10 2025

Keywords

Comments

Numerators of Dirichlet g.f.: Sum_{n>=1} a(n)/n^s = zeta(s-4)^(1/2).

Crossrefs

Cf. A000583, A383792 (denominators).

Programs

  • PARI
    for(n=1, 100, print1(numerator(direuler(p=2, n, 1/(1-p^4*X)^(1/2))[n]), ", "))

Formula

Sum_{k=1..n} A383791(k) / A383792(k) ~ n^5 / (5*sqrt(Pi*log(n))) * (1 + (1/5 - gamma/2)/(2*log(n))), where gamma is the Euler-Mascheroni constant A001620.
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