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.

Showing 1-2 of 2 results.

A329462 Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*j^2))).

Original entry on oeis.org

1, 1, 1, 2, 2, 1, 1, 2, 2, 3, 1, 2, 2, 2, 2, 3, 2, 2, 1, 5, 2, 1, 1, 2, 4, 4, 2, 3, 3, 5, 1, 3, 1, 3, 3, 4, 2, 2, 3, 6, 3, 4, 1, 2, 5, 3, 1, 3, 3, 8, 3, 6, 3, 4, 3, 4, 2, 4, 2, 7, 3, 4, 4, 4, 7, 4, 1, 5, 3, 7, 2, 4, 2, 6, 7, 3, 3, 9, 3, 8, 5, 5, 2, 7, 6, 4, 5, 3, 4, 14
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 13 2019

Keywords

Comments

Inverse Moebius transform of A033461.

Crossrefs

Cf. A033461, A047966, A047968, A329439.

Programs

  • Mathematica
    nmax = 90; CoefficientList[Series[Sum[-1 + Product[(1 + x^(k j^2)), {j, 1, Floor[nmax^(1/2)] + 1}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Formula

G.f.: Sum_{k>=1} A033461(k) * x^k / (1 - x^k).
a(n) = Sum_{d|n} A033461(d).

A329465 Expansion of Sum_{k>=1} (-1 + Product_{j>=1} 1 / (1 - x^(k*j*(j + 1)/2))).

Original entry on oeis.org

1, 2, 3, 4, 3, 8, 5, 8, 9, 11, 8, 20, 12, 17, 20, 25, 18, 36, 25, 38, 39, 44, 37, 68, 51, 63, 69, 85, 69, 113, 90, 117, 117, 136, 128, 189, 154, 185, 195, 239, 206, 288, 253, 308, 321, 358, 333, 457, 406, 476, 485, 566, 521, 671, 629, 734, 737, 833, 794, 1019
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 13 2019

Keywords

Comments

Inverse Moebius transform of A007294.

Crossrefs

Cf. A007294, A047966, A047968, A329439, A329466.

Programs

  • Mathematica
    nmax = 60; CoefficientList[Series[Sum[-1 + Product[1/(1 - x^(k j (j + 1)/2)), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Formula

G.f.: Sum_{k>=1} A007294(k) * x^k / (1 - x^k).
a(n) = Sum_{d|n} A007294(d).
Showing 1-2 of 2 results.

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