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 1-5 of 5 results.

A386748 a(n) = n^3*sigma_4(n).

Original entry on oeis.org

0, 1, 136, 2214, 17472, 78250, 301104, 823886, 2236928, 4842747, 10642000, 19488502, 38683008, 62750714, 112048496, 173245500, 286330880, 410343586, 658613592, 893878598, 1367184000, 1824083604, 2650436272, 3404837614, 4952558592, 6113296875, 8534097104, 10591107372
Offset: 0

Views

Author

Vaclav Kotesovec, Aug 01 2025

Keywords

Links

Crossrefs

Cf. A000578, A001159, A386749, A386747.

Programs

  • Magma
    [0] cat [n^3*DivisorSigma(4, n): n in [1..35]]; // Vincenzo Librandi, Aug 02 2025
  • Mathematica
    Table[n^3*DivisorSigma[4, n], {n, 0, 40}]
nmax = 40; CoefficientList[Series[Sum[k^7*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^7*x^k*(x^(2*k) + 4*x^k + 1)/(1 - x^k)^4. - Amiram Eldar, Aug 01 2025
a(n) = n^3*A001159(n).
Dirichlet g.f.: zeta(s-3)*zeta(s-7). - R. J. Mathar, Aug 03 2025

A386747 a(n) = n^2*sigma_4(n).

Original entry on oeis.org

0, 1, 68, 738, 4368, 15650, 50184, 117698, 279616, 538083, 1064200, 1771682, 3223584, 4826978, 8003464, 11549700, 17895680, 24137858, 36589644, 47046242, 68359200, 86861124, 120474376, 148036418, 206356608, 244531875, 328234504, 392263236, 514104864, 594824162
Offset: 0

Views

Author

Vaclav Kotesovec, Aug 01 2025

Keywords

Links

Crossrefs

Cf. A000290, A001159, A386749, A386748.

Programs

  • Magma
    [0] cat [n^2*DivisorSigma(4, n): n in [1..35]]; // Vincenzo Librandi, Aug 02 2025
  • Mathematica
    Table[n^2*DivisorSigma[4, n], {n, 0, 40}]
nmax = 40; CoefficientList[Series[Sum[k^6*x^k*(1 + x^k)/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=1} k^6*x^k*(1 + x^k)/(1 - x^k)^3. - Amiram Eldar, Aug 01 2025
a(n) = n^2*A001159(n).
Dirichlet g.f.: zeta(s-2)*zeta(s-6).- R. J. Mathar, Aug 03 2025

A386750 a(n) = n*sigma_6(n).

Original entry on oeis.org

0, 1, 130, 2190, 16644, 78130, 284700, 823550, 2130440, 4789539, 10156900, 19487182, 36450360, 62748530, 107061500, 171104700, 272696336, 410338690, 622640070, 893871758, 1300395720, 1803574500, 2533333660, 3404825470, 4665663600, 6103906275, 8157308900, 10474721820
Offset: 0

Views

Author

Vaclav Kotesovec, Aug 01 2025

Keywords

Links

Crossrefs

Cf. A013954.
Cf. A064987, A328259, A281372, A386749, A282050, A282060, A386751.

Programs

  • Magma
    [0] cat [n*DivisorSigma(6,n): n in [1..25]]; // Vincenzo Librandi, Aug 02 2025
  • Mathematica
    Table[n*DivisorSigma[6, n], {n, 0, 40}]
nmax = 40; CoefficientList[Series[x*Sum[k^7*x^(k-1)/(1 - x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=1} k^7*x^(k-1)/(1 - x^k)^2.
a(n) = n*A013954(n).
Dirichlet g.f.: zeta(s-1)*zeta(s-7). - R. J. Mathar, Aug 03 2025

A386751 a(n) = n*sigma_8(n).

Original entry on oeis.org

0, 1, 514, 19686, 263172, 1953130, 10118604, 40353614, 134744072, 387479547, 1003908820, 2357947702, 5180803992, 10604499386, 20741757596, 38449317180, 68988964880, 118587876514, 199164487158, 322687697798, 514009128360, 794401245204, 1211985118828, 1801152661486
Offset: 0

Views

Author

Vaclav Kotesovec, Aug 01 2025

Keywords

Links

Crossrefs

Cf. A013956.
Cf. A064987, A328259, A281372, A386749, A282050, A386750, A282060.

Programs

  • Magma
    [0] cat [n*DivisorSigma(8,n): n in [1..25]]; // Vincenzo Librandi, Aug 02 2025
  • Mathematica
    Table[n*DivisorSigma[8, n], {n, 0, 40}]
nmax = 40; CoefficientList[Series[x*Sum[k^9*x^(k-1)/(1 - x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=1} k^9*x^(k-1)/(1 - x^k)^2.
a(n) = n*A013956(n).
Dirichlet g.f.: zeta(s-1)*zeta(s-9). - R. J. Mathar, Aug 03 2025

A386784 a(n) = n^4*sigma_4(n).

Original entry on oeis.org

0, 1, 272, 6642, 69888, 391250, 1806624, 5767202, 17895424, 43584723, 106420000, 214373522, 464196096, 815759282, 1568678944, 2598682500, 4581294080, 6975840962, 11855044656, 16983693362, 27343680000, 38305755684, 58309597984, 78311265122, 118861406208, 152832421875
Offset: 0

Views

Author

Vaclav Kotesovec, Aug 02 2025

Keywords

Links

Crossrefs

Cf. A280022, A386783, A280025, A386785, A386786, A386787, A386788.
Cf. A001159, A386749, A386747, A386748.

Programs

  • Magma
    [0] cat [n^4*DivisorSigma(4, n): n in [1..35]]; // Vincenzo Librandi, Aug 03 2025
  • Mathematica
    Table[n^4*DivisorSigma[4, n], {n, 0, 40}]
nmax = 40; CoefficientList[Series[Sum[k^4*x^k*(1 + 247*x^k + 4293*x^(2*k) + 15619*x^(3*k) + 15619*x^(4*k) + 4293*x^(5*k) + 247*x^(6*k) + x^(7*k))/(1 - x^k)^9, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=1} k^4*x^k*(1 + 247*x^k + 4293*x^(2*k) + 15619*x^(3*k) + 15619*x^(4*k) + 4293*x^(5*k) + 247*x^(6*k) + x^(7*k))/(1 - x^k)^9.
a(n) = n^4*A001159(n).
Dirichlet g.f.: zeta(s-4)*zeta(s-8). - R. J. Mathar, Aug 03 2025
Showing 1-5 of 5 results.

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