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.

A386746 a(n) = n^3*sigma_2(n).

Original entry on oeis.org

0, 1, 40, 270, 1344, 3250, 10800, 17150, 43520, 66339, 130000, 162382, 362880, 373490, 686000, 877500, 1396736, 1424770, 2653560, 2482958, 4368000, 4630500, 6495280, 6448510, 11750400, 10171875, 14939600, 16140060, 23049600, 20535538, 35100000, 28658942, 44728320
Offset: 0

Views

Author

Vaclav Kotesovec, Aug 01 2025

Keywords

Links

Crossrefs

Cf. A001157, A328259, A386745.

Programs

  • Magma
    [0] cat [n^3*DivisorSigma(2, n): n in [1..35]]; // Vincenzo Librandi, Aug 02 2025
  • Mathematica
    Table[n^3*DivisorSigma[2, n], {n, 0, 40}]
nmax = 40; CoefficientList[Series[Sum[k^5*x^k*(x^(2*k) + 4*x^k + 1)/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=1} k^5*x^k*(x^(2*k) + 4*x^k + 1)/(1 - x^k)^4. - Amiram Eldar, Aug 01 2025
a(n) = n^3*A001157(n).
Dirichlet g.f.: zeta(s-3)*zeta(s-5). - R. J. Mathar, Aug 03 2025

A386783 a(n) = n^4*sigma_2(n).

Original entry on oeis.org

0, 1, 80, 810, 5376, 16250, 64800, 120050, 348160, 597051, 1300000, 1786202, 4354560, 4855370, 9604000, 13162500, 22347776, 24221090, 47764080, 47176202, 87360000, 97240500, 142896160, 148315730, 282009600, 254296875, 388429600, 435781620, 645388800, 595530602, 1053000000
Offset: 0

Views

Author

Vaclav Kotesovec, Aug 02 2025

Keywords

Links

Crossrefs

Cf. A280022, A280025, A386784, A386785, A386786, A386787, A386788.
Cf. A001157, A328259, A386745, A386746.

Programs

  • Magma
    [0] cat [n^4*DivisorSigma(2, n): n in [1..35]]; // Vincenzo Librandi, Aug 03 2025
  • Mathematica
    Table[n^4*DivisorSigma[2, n], {n, 0, 40}]
nmax = 40; CoefficientList[Series[Sum[k^4*x^k*(1 + 57*x^k + 302*x^(2*k) + 302*x^(3*k) + 57*x^(4*k) + x^(5*k)) / (1 - x^k)^7, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=1} k^4*x^k*(1 + 57*x^k + 302*x^(2*k) + 302*x^(3*k) + 57*x^(4*k) + x^(5*k)) / (1 - x^k)^7.
a(n) = n^4*A001157(n).
Dirichlet g.f.: zeta(s-4)*zeta(s-6). - R. J. Mathar, Aug 03 2025

A386777 a(n) = n^2*sigma_6(n).

Original entry on oeis.org

0, 1, 260, 6570, 66576, 390650, 1708200, 5764850, 17043520, 43105851, 101569000, 214359002, 437404320, 815730890, 1498861000, 2566570500, 4363141376, 6975757730, 11207521260, 16983563402, 26007914400, 37875064500, 55733340520, 78310985810, 111975926400, 152597656875
Offset: 0

Views

Author

Vaclav Kotesovec, Aug 02 2025

Keywords

Links

Crossrefs

Cf. A282097, A386745, A282099, A386747, A282751, A282753, A386778.
Cf. A013954, A386750.

Programs

  • Magma
    [0] cat [n^2*DivisorSigma(6, n): n in [1..35]]; // Vincenzo Librandi, Aug 04 2025
  • Mathematica
    Table[n^2*DivisorSigma[6, n], {n, 0, 30}]
nmax = 30; CoefficientList[Series[Sum[k^8*x^k*(1 + x^k)/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=1} k^8*x^k*(1 + x^k)/(1 - x^k)^3.
a(n) = n^2*A013954(n).
Dirichlet g.f.: zeta(s-2)*zeta(s-8). - R. J. Mathar, Aug 03 2025

A386778 a(n) = n^2*sigma_8(n).

Original entry on oeis.org

0, 1, 1028, 59058, 1052688, 9765650, 60711624, 282475298, 1077952576, 3487315923, 10039088200, 25937424722, 62169647904, 137858492018, 290384606344, 576739757700, 1103823438080, 2015993900738, 3584960768844, 6131066258162, 10280182567200, 16682426149284, 26663672614216
Offset: 0

Views

Author

Vaclav Kotesovec, Aug 02 2025

Keywords

Links

Crossrefs

Cf. A282097, A386745, A282099, A386747, A282751, A386777, A282753.
Cf. A013956, A386751.

Programs

  • Magma
    [0] cat [n^2*DivisorSigma(8, n): n in [1..35]]; // Vincenzo Librandi, Aug 04 2025
  • Mathematica
    Table[n^2*DivisorSigma[8, n], {n, 0, 30}]
nmax = 30; CoefficientList[Series[Sum[k^10*x^k*(1 + x^k)/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=1} k^10*x^k*(1 + x^k)/(1 - x^k)^3.
a(n) = n^2*A013956(n).
Dirichlet g.f.: zeta(s-2)*zeta(s-10). - R. J. Mathar, Aug 03 2025
Showing 1-4 of 4 results.

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