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.

A386749 a(n) = n*sigma_4(n).

Original entry on oeis.org

0, 1, 34, 246, 1092, 3130, 8364, 16814, 34952, 59787, 106420, 161062, 268632, 371306, 571676, 769980, 1118480, 1419874, 2032758, 2476118, 3417960, 4136244, 5476108, 6436366, 8598192, 9781275, 12624404, 14528268, 18360888, 20511178, 26179320, 28629182, 35791392, 39621252
Offset: 0

Views

Author

Vaclav Kotesovec, Aug 01 2025

Keywords

Links

Crossrefs

Cf. A064987, A328259, A281372, A282050, A386750, A282060, A386751.
Cf. A001159, A386747, A386748.

Programs

  • Magma
    [0] cat [n*DivisorSigma(4, n): n in [1..35]]; // Vincenzo Librandi, Aug 02 2025
  • Mathematica
    Table[n*DivisorSigma[4, n], {n, 0, 50}]
nmax = 50; CoefficientList[Series[x*Sum[k^5*x^(k-1)/(1 - x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x]
  • PARI
    a(n) = if (n, n*sigma(n,4), 0); \\ Michel Marcus, Aug 02 2025

Formula

G.f.: Sum_{k>=1} k^5*x^(k-1)/(1 - x^k)^2.
a(n) = n*A001159(n).
Dirichlet g.f.: zeta(s-1)*zeta(s-5). - 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

A386788 a(n) = n^4*sigma_8(n).

Original entry on oeis.org

0, 1, 4112, 531522, 16843008, 244141250, 2185618464, 13841289602, 68988964864, 282472589763, 1003908820000, 3138428391362, 8952429298176, 23298085151042, 56915382843424, 129766445482500, 282578800148480, 582622237313282, 1161527289105456, 2213314919196482, 4112073026880000
Offset: 0

Views

Author

Vaclav Kotesovec, Aug 02 2025

Keywords

Links

Crossrefs

Cf. A280022, A386783, A280025, A386784, A386785, A386786, A386787.
Cf. A013956, A386751, A386778, A386782.

Programs

  • Magma
    [0] cat [n^4*DivisorSigma(8, n): n in [1..35]]; // Vincenzo Librandi, Aug 03 2025
  • Mathematica
    Table[n^4*DivisorSigma[8, n], {n, 0, 30}]
nmax = 30; CoefficientList[Series[Sum[k^4*x^k*(1 + 4083*x^k + 478271*x^(2*k) + 10187685*x^(3*k) + 66318474*x^(4*k) + 162512286*x^(5*k) + 162512286*x^(6*k) + 66318474*x^(7*k) + 10187685*x^(8*k) + 478271*x^(9*k) + 4083*x^(10*k) + x^(11*k))/(1 - x^k)^13, {k, 1, nmax}], {x, 0, nmax}], x]
  • PARI
    a(n) = if (n, n^4*sigma(n,8), 0); \\ Michel Marcus, Aug 03 2025

Formula

G.f.: Sum_{k>=1} k^4*x^k*(1 + 4083*x^k + 478271*x^(2*k) + 10187685*x^(3*k) + 66318474*x^(4*k) + 162512286*x^(5*k) + 162512286*x^(6*k) + 66318474*x^(7*k) + 10187685*x^(8*k) + 478271*x^(9*k) + 4083*x^(10*k) + x^(11*k))/(1 - x^k)^13.
a(n) = n^4*A013956(n).
Dirichlet g.f.: zeta(s-4)*zeta(s-12). - 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

A386782 a(n) = n^3*sigma_8(n).

Original entry on oeis.org

0, 1, 2056, 177174, 4210752, 48828250, 364269744, 1977327086, 8623620608, 31385843307, 100390882000, 285311671942, 746035774848, 1792160396234, 4065384488816, 8651096365500, 17661175009280, 34271896312546, 64529293839192, 116490258905078, 205603651344000, 350330949134964
Offset: 0

Views

Author

Vaclav Kotesovec, Aug 02 2025

Keywords

Links

Crossrefs

Cf. A282211, A386746, A282213, A386748, A282781, A386780, A386781.
Cf. A013956, A386751, A386778.

Programs

  • Magma
    [0] cat [n^3*DivisorSigma(8, n): n in [1..35]]; // Vincenzo Librandi, Aug 04 2025
  • Mathematica
    Table[n^3*DivisorSigma[8, n], {n, 0, 30}]
nmax = 30; CoefficientList[Series[Sum[k^11*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^11*x^k*(x^(2*k) + 4*x^k + 1)/(1 - x^k)^4.
a(n) = n^3*A013956(n).
Dirichlet g.f.: zeta(s-3)*zeta(s-11). - R. J. Mathar, Aug 03 2025
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.