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 1-6 of 6 results.

A359233 Number of divisors of 5*n-1 of form 5*k+1.

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Dec 22 2022

Keywords

Comments

Also number of divisors of 5*n-1 of form 5*k+4.

Links

Crossrefs

Cf. A078703, A099774, A359211.
Cf. A001876, A001899, A359236, A359237, A359238.

Programs

  • Mathematica
    a[n_] := DivisorSum[5*n-1, 1 &, Mod[#, 5] == 1 &]; Array[a, 100] (* Amiram Eldar, Aug 23 2023 *)
  • PARI
    a(n) = sumdiv(5*n-1, d, d%5==1);
  • PARI
    a(n) = sumdiv(5*n-1, d, d%5==4);
  • PARI
    my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-x^(5*k-1))))
  • PARI
    my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^(4*k-3)/(1-x^(5*k-4))))

Formula

a(n) = A001876(5*n-1) = A001899(5*n-1).
G.f.: Sum_{k>0} x^k/(1 - x^(5*k-1)).
G.f.: Sum_{k>0} x^(4*k-3)/(1 - x^(5*k-4)).

A359236 Number of divisors of 5*n-2 of form 5*k+1.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 1, 2, 2, 1, 3, 2, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 4, 1, 3, 2, 1, 1, 3, 1, 1, 2, 2, 2, 3, 1, 1, 3, 1, 1, 5, 1, 1, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 1, 3, 3, 1, 4, 1, 1, 2, 1, 2, 4, 1, 2, 2, 1, 1, 3, 1, 3
Offset: 1

Views

Author

Seiichi Manyama, Dec 22 2022

Keywords

Comments

Also number of divisors of 5*n-2 of form 5*k+3.

Links

Crossrefs

Cf. A001876, A001878, A359233, A359237, A359238.

Programs

  • Mathematica
    a[n_] := DivisorSum[5*n-2, 1 &, Mod[#, 5] == 1 &]; Array[a, 100] (* Amiram Eldar, Aug 23 2023 *)
  • PARI
    a(n) = sumdiv(5*n-2, d, d%5==1);
  • PARI
    a(n) = sumdiv(5*n-2, d, d%5==3);
  • PARI
    my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-x^(5*k-2))))
  • PARI
    my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^(3*k-2)/(1-x^(5*k-4))))

Formula

a(n) = A001876(5*n-2) = A001878(5*n-2).
G.f.: Sum_{k>0} x^k/(1 - x^(5*k-2)).
G.f.: Sum_{k>0} x^(3*k-2)/(1 - x^(5*k-4)).

A359237 Number of divisors of 5*n-3 of form 5*k+1.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 2, 2, 1, 2, 1, 3, 1, 3, 1, 2, 1, 4, 1, 2, 2, 2, 1, 3, 1, 2, 1, 3, 2, 4, 1, 2, 1, 2, 2, 3, 1, 2, 1, 3, 1, 5, 1, 2, 1, 3, 1, 3, 2, 2, 2, 2, 1, 4, 1, 3, 1, 2, 1, 3, 1, 4, 3, 2, 1, 4, 1, 2, 1, 3, 1, 3, 2, 2, 1, 2, 2, 5, 1, 3, 1
Offset: 1

Views

Author

Seiichi Manyama, Dec 22 2022

Keywords

Comments

Also number of divisors of 5*n-3 of form 5*k+2.

Links

Crossrefs

Cf. A001876, A001877, A359233, A359236, A359238.

Programs

  • Mathematica
    a[n_] := DivisorSum[5*n-3, 1 &, Mod[#, 5] == 1 &]; Array[a, 100] (* Amiram Eldar, Aug 23 2023 *)
  • PARI
    a(n) = sumdiv(5*n-3, d, d%5==1);
  • PARI
    a(n) = sumdiv(5*n-3, d, d%5==2);
  • PARI
    my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-x^(5*k-3))))
  • PARI
    my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^(2*k-1)/(1-x^(5*k-4))))

Formula

a(n) = A001876(5*n-3) = A001877(5*n-3).
G.f.: Sum_{k>0} x^k/(1 - x^(5*k-3)).
G.f.: Sum_{k>0} x^(2*k-1)/(1 - x^(5*k-4)).

A364095 Sum of divisors of 5*n-4 of form 5*k+1.

Original entry on oeis.org

1, 7, 12, 17, 22, 27, 32, 43, 42, 47, 52, 57, 62, 84, 72, 77, 82, 87, 92, 119, 102, 107, 112, 117, 133, 154, 132, 137, 142, 147, 152, 189, 162, 167, 172, 204, 182, 224, 192, 197, 202, 207, 212, 259, 222, 227, 264, 237, 242, 294, 252, 273, 262, 267, 272, 329, 282, 324, 292, 297, 302, 364, 312
Offset: 1

Views

Author

Seiichi Manyama, Jul 04 2023

Keywords

Crossrefs

Cf. A364092, A364093, A364094.
Cf. A284097, A359238, A364099.

Programs

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

Formula

a(n) = A284097(5*n-4).
G.f.: Sum_{k>0} (5*k-4) * x^k / (1 - x^(5*k-4)).

A364099 Expansion of Sum_{k>0} k * x^k / (1 - x^(5*k-4)).

Original entry on oeis.org

1, 3, 4, 5, 6, 7, 8, 11, 10, 11, 12, 13, 14, 20, 16, 17, 18, 19, 20, 27, 22, 23, 24, 25, 29, 34, 28, 29, 30, 31, 32, 41, 34, 35, 36, 44, 38, 48, 40, 41, 42, 43, 44, 55, 46, 47, 56, 49, 50, 62, 52, 57, 54, 55, 56, 69, 58, 68, 60, 61, 62, 76, 64, 65, 66, 67, 68, 92, 80, 71, 72, 73, 74
Offset: 1

Views

Author

Seiichi Manyama, Jul 04 2023

Keywords

Crossrefs

Cf. A359238, A364095.

Programs

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

Formula

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

A363853 Number of divisors of 7*n-6 of form 7*k+1.

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Jun 24 2023

Keywords

Crossrefs

Cf. A359212, A359238, A359309.
Cf. A279061.

Programs

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

Formula

a(n) = A279061(7*n-6).
G.f.: Sum_{k>0} x^k/(1 - x^(7*k-6)).
Showing 1-6 of 6 results.

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