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.

A363259 Expansion of Sum_{k>0} k * x^(2*k) / (1 - x^(4*k-1)).

Original entry on oeis.org

0, 1, 0, 2, 1, 3, 0, 5, 0, 5, 3, 6, 0, 8, 0, 8, 4, 11, 0, 11, 0, 11, 5, 12, 2, 14, 0, 17, 6, 15, 0, 19, 0, 17, 7, 18, 0, 24, 5, 20, 8, 21, 0, 23, 0, 25, 9, 29, 0, 29, 0, 26, 16, 27, 0, 29, 0, 35, 11, 32, 3, 32, 0, 32, 12, 33, 7, 46, 0, 35, 13, 39, 0, 40, 0, 38, 14, 47, 0, 41, 8, 41, 22, 42, 0, 49, 0
Offset: 1

Views

Author

Seiichi Manyama, Jul 08 2023

Keywords

Crossrefs

Cf. A364084, A364085.
Cf. A363392.

Programs

  • Mathematica
    a[n_] := DivisorSum[4*n - 2, # + 1 &, Mod[#, 4] == 3 &]/4; Array[a, 100] (* Amiram Eldar, Jul 08 2023 *)
  • PARI
    a(n) = sumdiv(4*n-2, d, (d%4==3)*(d+1))/4;

Formula

a(n) = (1/4) * Sum_{d | 4*n-2, d==3 (mod 4)} (d+1).
G.f.: Sum_{k>0} x^(3*k-1) / (1 - x^(4*k-2))^2.

A363407 Sum of divisors of 4*n-3 of form 4*k+3.

Original entry on oeis.org

0, 0, 3, 0, 0, 10, 0, 0, 14, 0, 0, 18, 7, 0, 22, 0, 0, 26, 0, 18, 30, 0, 0, 34, 0, 0, 60, 0, 0, 42, 11, 0, 46, 26, 0, 50, 0, 0, 54, 0, 30, 84, 0, 0, 62, 0, 0, 100, 0, 0, 70, 0, 30, 74, 38, 0, 93, 0, 0, 82, 0, 42, 86, 34, 0, 90, 0, 0, 140, 0, 0, 132, 0, 0, 140, 50, 0, 106, 0, 0, 110, 0, 54, 114, 0, 42, 156
Offset: 1

Views

Author

Seiichi Manyama, Jul 08 2023

Keywords

Crossrefs

Cf. A050452, A359240, A364084.

Programs

  • Mathematica
    a[n_] := DivisorSum[4*n - 3, # &, Mod[#, 4] == 3 &]; Array[a, 100] (* Amiram Eldar, Jul 08 2023 *)
  • PARI
    a(n) = sumdiv(4*n-3, d, (d%4==3)*d);

Formula

a(n) = A050452(4*n-3).
G.f.: Sum_{k>0} (4*k-1) * x^(3*k) / (1 - x^(4*k-1)).
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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