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 1-3 of 3 results.

A074285 Sum of the divisors of n-th triangular number.

Original entry on oeis.org

1, 4, 12, 18, 24, 32, 56, 91, 78, 72, 144, 168, 112, 192, 360, 270, 234, 260, 360, 576, 384, 288, 672, 868, 434, 560, 960, 720, 720, 768, 992, 1488, 864, 864, 1872, 1482, 760, 1120, 2352, 1764, 1344, 1408, 1584, 2808, 1872, 1152, 2880, 3420, 1767, 2232
Offset: 1

Views

Author

Shyam Sunder Gupta, Sep 21 2002

Keywords

Comments

By definition a(n) is also the sum of the divisors of n-th generalized hexagonal number. - Omar E. Pol, Nov 24 2015

Examples

			a(4)=18 because the sum of divisors of the 4th triangular number (i.e., 10) is 1 + 2 + 5 + 10 = 18.

Links

Crossrefs

Cf. A000203, A000217, A330322.

Programs

  • Mathematica
    Table[DivisorSigma[1, n*(n + 1)/2], {n, 1, 100}] (* Vaclav Kotesovec, Aug 18 2021 *)
  • PARI
    a(n) = sigma(n*(n+1)/2); \\ Altug Alkan, Nov 24 2015

Formula

a(n) = A000203(A000217(n)). - Omar E. Pol, Nov 24 2015
Sum_{k=1..n} a(k) ~ n^3/3. - Vaclav Kotesovec, Aug 18 2021

A083539 a(n) = sigma(n) * sigma(n+1): product of sigma-values for consecutive integers.

Original entry on oeis.org

3, 12, 28, 42, 72, 96, 120, 195, 234, 216, 336, 392, 336, 576, 744, 558, 702, 780, 840, 1344, 1152, 864, 1440, 1860, 1302, 1680, 2240, 1680, 2160, 2304, 2016, 3024, 2592, 2592, 4368, 3458, 2280, 3360, 5040, 3780, 4032, 4224, 3696, 6552, 5616, 3456, 5952
Offset: 1

Views

Author

Labos Elemer, May 21 2003

Keywords

Links

Crossrefs

Cf. A000203, A002378, A060781, A060780, A083538, A330322 (partial sums).
Cf. A083481, A083542, A092517.

Programs

  • Mathematica
    f[x_] := DivisorSigma[1, x]; t=Table[f[w+1]*f[w], {w, 1, 128}]
Times@@@Partition[DivisorSigma[1,Range[50]],2,1] (* Harvey P. Dale, May 21 2014 *)
  • PARI
    a(n)=sigma(n)*sigma(n+1) \\ Charles R Greathouse IV, Feb 14 2013

Formula

a(n) = A000203(A002378(n)). - Amiram Eldar, Jul 10 2024

A347108 a(n) = Sum_{k=1..n} sigma(k)*sigma(2*k), where sigma(n) = A000203(n) is the sum of the divisors of n.

Original entry on oeis.org

3, 24, 72, 177, 285, 621, 813, 1278, 1785, 2541, 2973, 4653, 5241, 6585, 8313, 10266, 11238, 14787, 15987, 19767, 22839, 25863, 27591, 35031, 37914, 42030, 46830, 53550, 56250, 68346, 71418, 79419, 86331, 93135, 100047, 117792, 122124, 130524, 139932, 156672
Offset: 1

Views

Author

Vaclav Kotesovec, Aug 18 2021

Keywords

Crossrefs

Cf. A000203, A024916, A065764, A072379, A074285, A326123, A326124, A330322, A346865.

Programs

  • Mathematica
    Accumulate[Table[DivisorSigma[1,k] * DivisorSigma[1,2*k], {k, 1, 100}]]
  • PARI
    a(n) = sum(k=1, n, sigma(k)*sigma(2*k)); \\ Michel Marcus, Aug 18 2021

Formula

a(n) ~ 2*zeta(3)*n^3.
Showing 1-3 of 3 results.

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

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