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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A034779 Dirichlet convolution of [ 1,1,1,... ] with A034778.

Original entry on oeis.org

1, -47, 505, -2415, 9661, -23735, -33487, 237201, -163277, -454067, 1069225, -1219575, -1155475, 1573889, 4878805, 323217, -13811867, 7674019, 21322841, -23331315, -16910935, -50253575, 37286545, 119786505
Offset: 1

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Author

Keywords

Comments

Multiplicative because both A000012 and A034778 are. - Christian G. Bower, May 16 2005

Crossrefs

Programs

  • Mathematica
    b[n_] := DivisorSum[n, RamanujanTau[#] RamanujanTau[n/#]&];
    a[n_] := DivisorSum[n, b];
    a /@ Range[1, 24] (* Jean-François Alcover, Sep 20 2019 *)
  • PARI
    seq(n)={my(v=Vec(eta(x + O(x^n))^24)); dirmul(dirmul(v,v), vector(#v,n,1))} \\ Andrew Howroyd, Feb 12 2018

Extensions

Offset corrected by Andrew Howroyd, Feb 11 2018

A308492 Expansion of Sum_{i>=1} mu(i) * x^i * Product_{j>=1} (1 - x^(i*j))^24.

Original entry on oeis.org

1, -25, 251, -1448, 4829, -6275, -16745, 85952, -113895, -120725, 534611, -363448, -577739, 418625, 1212079, 902656, -6905935, 2847375, 10661419, -6992392, -4202995, -13365275, 18643271, 21573952, -25504055, 14443475, -73165437, 24246760, 128406629, -30301975
Offset: 1

Views

Author

Ilya Gutkovskiy, May 31 2019

Keywords

Comments

Moebius transform of A000594.

Examples

			G.f. = x - 25*x^2 + 251*x^3 - 1448*x^4 + 4829*x^5 - 6275*x^6 - 16745*x^7 + 85952*x^8 - 113895*x^9 - 120725*x^10 + ...
		

Crossrefs

Programs

  • Mathematica
    nmax = 30; CoefficientList[Series[Sum[MoebiusMu[i] x^i Product[(1 - x^(i j))^24, {j, 1, nmax}], {i, 1, nmax}], {x, 0, nmax}], x] // Rest
    a[n_] := Sum[MoebiusMu[n/d] RamanujanTau[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 30}]
  • PARI
    a(n) = sumdiv(n, d, moebius(n/d)*ramanujantau(d)); \\ Michel Marcus, Jun 01 2019

Formula

a(n) = Sum_{d|n} mu(n/d)*A000594(d).
Showing 1-2 of 2 results.