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 1-3 of 3 results.

A363028 Expansion of Sum_{k>0} k * x^(2*k-1) / (1 - x^(5*k-3)).

Original entry on oeis.org

1, 0, 3, 0, 4, 0, 5, 0, 6, 2, 7, 0, 8, 0, 9, 0, 15, 0, 11, 0, 12, 0, 13, 6, 14, 0, 15, 0, 19, 0, 24, 0, 18, 0, 19, 0, 20, 8, 21, 0, 29, 0, 23, 0, 33, 0, 25, 0, 26, 0, 27, 10, 36, 0, 29, 0, 30, 4, 42, 0, 32, 0, 33, 0, 43, 12, 35, 0, 36, 0, 37, 0, 51, 0, 48, 0, 50, 0, 41, 14, 42, 0, 43, 0, 44, 0, 60, 0
Offset: 1

Views

Author

Seiichi Manyama, Jul 06 2023

Keywords

Links

Crossrefs

Cf. A359287, A362952.
Cf. A363155, A364096, A364104.

Programs

  • Mathematica
    a[n_] := DivisorSum[5*n - 1, # + 3 &, Mod[#, 5] == 2 &]/5; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)
  • PARI
    a(n) = sumdiv(5*n-1, d, (d%5==2)*(d+3))/5;

Formula

a(n) = (1/5) * Sum_{d | 5*n-1, d==2 (mod 5)} (d+3).
G.f.: Sum_{k>0} x^(2*k-1) / (1 - x^(5*k-3))^2.

A359288 Number of divisors of 5*n-1 of form 5*k+3.

Original entry on oeis.org

0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 1, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 4, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 3, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, 0, 4, 0, 2, 4, 0, 0, 2, 0
Offset: 1

Views

Author

Seiichi Manyama, Dec 24 2022

Keywords

Links

Crossrefs

Cf. A001878.
Cf. A359233, A359287.
Cf. A359236, A359244, A359270.

Programs

  • Mathematica
    a[n_] := DivisorSum[5*n-1, 1 &, Mod[#, 5] == 3 &]; Array[a, 100] (* Amiram Eldar, Aug 16 2023 *)
  • PARI
    a(n) = sumdiv(5*n-1, d, d%5==3);
  • PARI
    my(N=100, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(3*k-1)/(1-x^(5*k-2)))))

Formula

a(n) = A001878(5*n-1).
G.f.: Sum_{k>0} x^(3*k-1)/(1 - x^(5*k-2)).

A362952 Sum of divisors of 5*n-1 of form 5*k+2.

Original entry on oeis.org

2, 0, 9, 0, 14, 0, 19, 0, 24, 7, 29, 0, 34, 0, 39, 0, 63, 0, 49, 0, 54, 0, 59, 24, 64, 0, 69, 0, 86, 0, 108, 0, 84, 0, 89, 0, 94, 34, 99, 0, 133, 0, 109, 0, 153, 0, 119, 0, 124, 0, 129, 44, 168, 0, 139, 0, 144, 17, 198, 0, 154, 0, 159, 0, 203, 54, 169, 0, 174, 0, 179, 0, 243, 0, 228, 0, 238, 0, 199, 64, 204
Offset: 1

Views

Author

Seiichi Manyama, Jul 06 2023

Keywords

Crossrefs

Cf. A363025, A363026, A363027.
Cf. A284280, A359287, A363028.

Programs

  • Mathematica
    a[n_] := DivisorSum[5*n - 1, # &, Mod[#, 5] == 2 &]; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)
  • PARI
    a(n) = sumdiv(5*n-1, d, (d%5==2)*d);

Formula

a(n) = A284280(5*n-1).
G.f.: Sum_{k>0} (5*k-3) * x^(2*k-1) / (1 - x^(5*k-3)).
Showing 1-3 of 3 results.

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

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