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 1-7 of 7 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.

A363155 Expansion of Sum_{k>0} k * x^(3*k-1) / (1 - x^(5*k-2)).

Original entry on oeis.org

0, 1, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 2, 6, 0, 0, 7, 0, 0, 8, 5, 0, 9, 0, 0, 10, 0, 0, 17, 0, 0, 12, 0, 3, 13, 0, 7, 14, 0, 0, 15, 0, 0, 16, 8, 0, 24, 0, 0, 18, 0, 0, 28, 0, 0, 20, 0, 0, 21, 8, 10, 22, 0, 0, 27, 0, 0, 24, 11, 0, 25, 0, 9, 26, 0, 0, 39, 0, 0, 28, 0, 0, 38, 0, 13, 40, 0, 0, 31, 0, 0
Offset: 1

Views

Author

Seiichi Manyama, Jul 06 2023

Keywords

Links

Crossrefs

Cf. A359288, A363033.
Cf. A363028, A364096, A364104.

Programs

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

Formula

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

A364096 Expansion of Sum_{k>0} k * x^(4*k-3) / (1 - x^(5*k-4)).

Original entry on oeis.org

1, 1, 1, 1, 3, 1, 1, 1, 4, 1, 3, 1, 5, 1, 1, 1, 8, 1, 1, 4, 7, 1, 3, 1, 8, 1, 1, 1, 15, 1, 4, 1, 10, 1, 3, 1, 11, 6, 1, 1, 14, 4, 1, 1, 17, 1, 9, 1, 14, 1, 1, 1, 20, 1, 1, 8, 16, 1, 8, 1, 21, 1, 1, 4, 28, 1, 1, 1, 19, 1, 3, 1, 26, 10, 4, 1, 27, 1, 1, 6, 22, 1, 13, 1, 23, 4, 8, 1, 26, 1, 1, 12, 29, 1, 3, 1
Offset: 1

Views

Author

Seiichi Manyama, Jul 04 2023

Keywords

Links

Crossrefs

Cf. A359233, A364092.
Cf. A363028, A363155, A364104.

Programs

  • Mathematica
    a[n_] := DivisorSum[5*n - 1, # + 4 &, Mod[#, 5] == 1 &]/5; Array[a, 100] (* Amiram Eldar, Jul 12 2023 *)
  • PARI
    a(n) = sumdiv(5*n-1, d, (d%5==1)*(d+4))/5;

Formula

a(n) = (1/5) * Sum_{d | 5*n-1, d==1 (mod 5)} (d+4).
G.f.: Sum_{k>0} x^k / (1 - x^(5*k-1))^2.

A364100 Sum of divisors of 5*n-1 of form 5*k+4.

Original entry on oeis.org

4, 9, 14, 19, 28, 29, 34, 39, 48, 49, 63, 59, 68, 69, 74, 79, 102, 89, 94, 108, 108, 109, 133, 119, 128, 129, 134, 139, 181, 149, 168, 159, 168, 169, 203, 179, 188, 198, 194, 199, 242, 228, 214, 219, 242, 229, 282, 239, 248, 249, 254, 259, 336, 269, 274, 288, 288, 289, 357, 299, 327, 309, 314, 348
Offset: 1

Views

Author

Seiichi Manyama, Jul 04 2023

Keywords

Crossrefs

Cf. A364101, A364102, A364103.
Cf. A284103, A359233, A364104.

Programs

  • Mathematica
    a[n_] := DivisorSum[5*n - 1, # &, Mod[#, 5] == 4 &]; Array[a, 100] (* Amiram Eldar, Jul 17 2023 *)
  • PARI
    a(n) = sumdiv(5*n-1, d, (d%5==4)*d);

Formula

a(n) = A284103(5*n-1).
G.f.: Sum_{k>0} (5*k-1) * x^k / (1 - x^(5*k-1)).

A364105 Expansion of Sum_{k>0} k * x^(2*k) / (1 - x^(5*k-1)).

Original entry on oeis.org

0, 1, 0, 2, 0, 4, 0, 4, 0, 6, 0, 6, 2, 8, 0, 8, 0, 10, 0, 13, 0, 14, 0, 12, 0, 14, 4, 14, 0, 16, 2, 16, 0, 26, 0, 18, 0, 20, 0, 22, 6, 22, 0, 22, 0, 28, 0, 34, 2, 26, 0, 26, 0, 28, 8, 28, 0, 37, 0, 30, 0, 44, 0, 32, 4, 34, 2, 34, 10, 42, 0, 36, 0, 38, 0, 54, 0, 40, 0, 40, 0, 54, 12, 46, 2, 44, 0, 44, 0
Offset: 1

Views

Author

Seiichi Manyama, Jul 05 2023

Keywords

Crossrefs

Cf. A364104, A364106, A364107.
Cf. A359269, A364101.

Programs

  • Mathematica
    a[n_] := DivisorSum[5*n - 2, # + 1 &, Mod[#, 5] == 4 &]/5; Array[a, 100] (* Amiram Eldar, Jul 12 2023 *)
  • PARI
    a(n) = sumdiv(5*n-2, d, (d%5==4)*(d+1))/5;

Formula

a(n) = (1/5) * Sum_{d | 5*n-2, d==4 (mod 5)} (d+1).
G.f.: Sum_{k>0} x^(4*k-2) / (1 - x^(5*k-3))^2.

A364106 Expansion of Sum_{k>0} k * x^(3*k) / (1 - x^(5*k-1)).

Original entry on oeis.org

0, 0, 1, 0, 0, 2, 1, 0, 3, 0, 1, 4, 0, 0, 8, 0, 0, 6, 1, 0, 7, 0, 4, 10, 0, 0, 10, 0, 0, 10, 5, 0, 13, 0, 1, 12, 3, 0, 19, 0, 0, 16, 1, 0, 15, 0, 7, 16, 0, 4, 23, 0, 0, 18, 8, 0, 19, 0, 1, 22, 0, 0, 35, 0, 3, 22, 1, 0, 29, 0, 10, 24, 0, 0, 26, 6, 0, 28, 14, 0, 27, 0, 1, 28, 0, 0, 48, 4, 7, 30, 1, 0
Offset: 1

Views

Author

Seiichi Manyama, Jul 05 2023

Keywords

Crossrefs

Cf. A364104, A364105, A364107.
Cf. A359270, A364102.

Programs

  • Mathematica
    a[n_] := DivisorSum[5*n - 3, # + 1 &, Mod[#, 5] == 4 &]/5; Array[a, 100] (* Amiram Eldar, Jul 12 2023 *)
  • PARI
    a(n) = sumdiv(5*n-3, d, (d%5==4)*(d+1))/5;

Formula

a(n) = (1/5) * Sum_{d | 5*n-3, d==4 (mod 5)} (d+1).
G.f.: Sum_{k>0} x^(4*k-1) / (1 - x^(5*k-2))^2.

A364107 Expansion of Sum_{k>0} k * x^(4*k) / (1 - x^(5*k-1)).

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 5, 2, 0, 0, 6, 0, 0, 0, 7, 0, 5, 0, 8, 0, 0, 0, 9, 0, 0, 6, 10, 0, 0, 0, 14, 0, 0, 0, 19, 0, 0, 0, 13, 0, 0, 0, 14, 8, 7, 0, 15, 0, 0, 0, 16, 0, 9, 0, 17, 0, 0, 0, 26, 0, 0, 10, 19, 4, 0, 0, 20, 0, 0, 0, 32, 0, 9, 0, 22, 0, 0, 0, 23, 12, 0, 0, 33, 0, 0, 0
Offset: 1

Views

Author

Seiichi Manyama, Jul 05 2023

Keywords

Crossrefs

Cf. A364104, A364105, A364106.
Cf. A359241, A364103.

Programs

  • Mathematica
    a[n_] := DivisorSum[5*n - 4, # + 1 &, Mod[#, 5] == 4 &]/5; Array[a, 100] (* Amiram Eldar, Jul 12 2023 *)
  • PARI
    a(n) = sumdiv(5*n-4, d, (d%5==4)*(d+1))/5;

Formula

a(n) = (1/5) * Sum_{d | 5*n-4, d==4 (mod 5)} (d+1).
G.f.: Sum_{k>0} x^(4*k) / (1 - x^(5*k-1))^2.
Showing 1-7 of 7 results.

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