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.

A359240 Number of divisors of 4*n-3 of form 4*k+3.

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Dec 22 2022

Keywords

Links

Crossrefs

Cf. A359239, A359241.
Cf. A001842.

Programs

  • Mathematica
    a[n_] := DivisorSum[4*n-3, 1 &, Mod[#, 4] == 3 &]; Array[a, 100] (* Amiram Eldar, Aug 23 2023 *)
  • PARI
    a(n) = sumdiv(4*n-3, d, d%4==3);
  • PARI
    my(N=100, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(3*k)/(1-x^(4*k-1)))))

Formula

a(n) = A001842(4*n-3).
G.f.: Sum_{k>0} x^(3*k)/(1 - x^(4*k-1)).

A359241 Number of divisors of 5*n-4 of form 5*k+4.

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Dec 22 2022

Keywords

Links

Crossrefs

Cf. A359239, A359240.
Cf. A001899.

Programs

  • Mathematica
    a[n_] := DivisorSum[5*n-4, 1 &, Mod[#, 5] == 4 &]; Array[a, 100] (* Amiram Eldar, Aug 23 2023 *)
  • PARI
    a(n) = sumdiv(5*n-4, d, d%5==4);
  • PARI
    my(N=100, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=1, N, x^(4*k)/(1-x^(5*k-1)))))

Formula

a(n) = A001899(5*n-4).
G.f.: Sum_{k>0} x^(4*k)/(1 - x^(5*k-1)).

A359327 Number of divisors of 6*n-5 of form 6*k+5.

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Dec 25 2022

Keywords

Links

Crossrefs

Cf. A319995, A359305, A359324, A359325, A359326.
Cf. A359239, A359240, A359241.

Programs

  • Mathematica
    a[n_] := DivisorSum[6*n-5, 1 &, Mod[#, 6] == 5 &]; Array[a, 100] (* Amiram Eldar, Aug 14 2023 *)
  • PARI
    a(n) = sumdiv(6*n-5, d, d%6==5);
  • PARI
    my(N=100, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(sum(k=1, N, x^(5*k)/(1-x^(6*k-1)))))

Formula

a(n) = A319995(6*n-5).
G.f.: Sum_{k>0} x^(5*k)/(1 - x^(6*k-1)).

A359324 Number of divisors of 6*n-2 of form 6*k+5.

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Dec 25 2022

Keywords

Links

Crossrefs

Cf. A319995, A359305, A359325, A359326, A359327.
Cf. A359239, A359269, A359290.

Programs

  • Mathematica
    a[n_] := DivisorSum[6*n-2, 1 &, Mod[#, 6] == 5 &]; Array[a, 100] (* Amiram Eldar, Aug 14 2023 *)
  • PARI
    a(n) = sumdiv(6*n-2, d, d%6==5);
  • PARI
    my(N=100, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(2*k)/(1-x^(6*k-1)))))
  • PARI
    my(N=100, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(5*k-3)/(1-x^(6*k-4)))))

Formula

a(n) = A319995(6*n-2).
G.f.: Sum_{k>0} x^(2*k)/(1 - x^(6*k-1)).
G.f.: Sum_{k>0} x^(5*k-3)/(1 - x^(6*k-4)).

A363858 Number of divisors of 7*n-6 of form 7*k+6.

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Jun 24 2023

Keywords

Crossrefs

Cf. A361691, A363854, A363855, A363856, A363857.
Cf. A359239, A359241, A359327.
Cf. A363808.

Programs

  • Mathematica
    a[n_] := DivisorSum[7*n - 6, 1 &, Mod[#, 7] == 6 &]; Array[a, 100] (* Amiram Eldar, Jun 25 2023 *)
  • PARI
    a(n) = sumdiv(7*n-6, d, d%7==6);

Formula

a(n) = A363808(7*n-6).
G.f.: Sum_{k>0} x^(6*k)/(1 - x^(7*k-1)).

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)).

A364067 Expansion of Sum_{k>0} k * x^(2*k) / (1 - x^(3*k-1)).

Original entry on oeis.org

0, 1, 0, 3, 0, 4, 0, 5, 2, 6, 0, 7, 0, 13, 0, 9, 0, 10, 6, 11, 0, 15, 0, 20, 0, 14, 0, 15, 8, 23, 0, 17, 0, 27, 0, 19, 0, 28, 10, 21, 4, 22, 0, 34, 0, 33, 0, 25, 12, 26, 0, 36, 0, 51, 0, 29, 0, 30, 14, 31, 0, 43, 10, 48, 0, 39, 0, 35, 16, 48, 0, 37, 0, 66, 0, 39, 0, 53, 18, 52, 0, 42, 0, 62, 12, 58, 0, 45
Offset: 1

Views

Author

Seiichi Manyama, Jul 04 2023

Keywords

Links

Crossrefs

Cf. A359239, A363891.
Cf. A364064, A364065, A364066.

Programs

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

Formula

a(n) = (1/3) * Sum_{d | 3*n-2, d==2 (mod 3)} (d+1).
G.f.: Sum_{k>0} x^(2*k) / (1 - x^(3*k-1))^2.
Showing 1-7 of 7 results.

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