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 1-4 of 4 results.

A363514 Sum of divisors of 3*n-1 of form 3*k+1.

Original entry on oeis.org

1, 1, 5, 1, 8, 1, 15, 1, 14, 1, 21, 8, 20, 1, 27, 1, 36, 1, 40, 1, 32, 14, 39, 1, 38, 8, 71, 1, 44, 1, 51, 20, 57, 1, 70, 1, 88, 1, 63, 8, 62, 26, 85, 1, 68, 1, 120, 14, 74, 1, 100, 32, 80, 8, 87, 1, 130, 1, 131, 1, 112, 38, 99, 1, 98, 1, 180, 8, 104, 20, 111, 44, 110, 14, 168, 1, 172, 1
Offset: 1

Views

Author

Seiichi Manyama, Jun 26 2023

Keywords

Links

Crossrefs

Cf. A363889, A363890, A363891.
Cf. A078181, A359211.

Programs

  • Mathematica
    a[n_] := DivisorSum[3*n - 1, # &, Mod[#, 3] == 1 &]; Array[a, 100] (* Amiram Eldar, Jun 26 2023 *)
  • PARI
    a(n) = sumdiv(3*n-1, d, (d%3==1)*d);

Formula

a(n) = A078181(3*n-1).
G.f.: Sum_{k>0} (3*k-2) * x^(2*k-1)/(1 - x^(3*k-2)).

A363889 Sum of divisors of 3*n-2 of form 3*k+1.

Original entry on oeis.org

1, 5, 8, 11, 14, 21, 20, 23, 26, 40, 32, 35, 38, 55, 44, 47, 57, 70, 56, 59, 62, 85, 68, 88, 74, 100, 80, 83, 86, 115, 112, 95, 98, 140, 104, 107, 110, 168, 116, 119, 122, 160, 128, 154, 160, 175, 140, 143, 146, 190, 152, 184, 158, 231, 164, 167, 183, 220, 208, 179, 182, 235, 188
Offset: 1

Views

Author

Seiichi Manyama, Jun 26 2023

Keywords

Links

Crossrefs

Cf. A363514, A363890, A363891.
Cf. A078181, A359212.

Programs

  • Mathematica
    a[n_] := DivisorSum[3*n - 2, # &, Mod[#, 3] == 1 &]; Array[a, 100] (* Amiram Eldar, Jun 26 2023 *)
  • PARI
    a(n) = sumdiv(3*n-2, d, (d%3==1)*d);

Formula

a(n) = A078181(3*n-2).
G.f.: Sum_{k>0} (3*k-2) * x^k/(1 - x^(3*k-2)).

A363891 Sum of divisors of 3*n-2 of form 3*k+2.

Original entry on oeis.org

0, 2, 0, 7, 0, 10, 0, 13, 5, 16, 0, 19, 0, 35, 0, 25, 0, 28, 16, 31, 0, 42, 0, 56, 0, 40, 0, 43, 22, 65, 0, 49, 0, 77, 0, 55, 0, 80, 28, 61, 11, 64, 0, 98, 0, 95, 0, 73, 34, 76, 0, 104, 0, 147, 0, 85, 0, 88, 40, 91, 0, 125, 28, 140, 0, 114, 0, 103, 46, 140, 0, 109, 0, 192, 0, 115, 0
Offset: 1

Views

Author

Seiichi Manyama, Jun 26 2023

Keywords

Links

Crossrefs

Cf. A363514, A363889, A363890.
Cf. A078182, A359239.

Programs

  • Mathematica
    a[n_] := DivisorSum[3*n - 2, # &, Mod[#, 3] == 2 &]; Array[a, 100] (* Amiram Eldar, Jun 26 2023 *)
  • PARI
    a(n) = sumdiv(3*n-2, d, (d%3==2)*d);

Formula

a(n) = A078182(3*n-2).
G.f.: Sum_{k>0} (3*k-1) * x^(2*k)/(1 - x^(3*k-1)).

A364066 Expansion of Sum_{k>0} k * x^k / (1 - x^(3*k-1)).

Original entry on oeis.org

1, 2, 4, 4, 6, 6, 10, 8, 10, 10, 15, 14, 14, 14, 20, 16, 20, 18, 28, 20, 22, 24, 30, 24, 26, 30, 40, 28, 30, 30, 40, 34, 39, 34, 48, 36, 44, 38, 50, 46, 42, 44, 58, 44, 46, 46, 74, 52, 50, 50, 68, 54, 54, 62, 70, 56, 66, 58, 82, 60, 76, 64, 80, 64, 66, 66, 97, 78, 70, 74, 90, 74, 74, 80, 114, 76, 88, 78, 100
Offset: 1

Views

Author

Seiichi Manyama, Jul 04 2023

Keywords

Links

Crossrefs

Cf. A364063, A364085.
Cf. A359211, A363890.

Programs

  • Mathematica
    a[n_] := DivisorSum[3*n - 1, # + 1 &, Mod[#, 3] == 2 &]/3; Array[a, 100] (* Amiram Eldar, Jul 05 2023 *)
  • PARI
    a(n) = sumdiv(3*n-1, d, (d%3==2)*(d+1))/3;

Formula

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

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