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.

A367506 a(n) = Sum_{d|n} (d+n)^n.

Original entry on oeis.org

2, 25, 280, 6017, 107776, 3897218, 107510656, 4867995713, 204519070720, 10904505179450, 585061309782016, 38168392129581810, 2481946587976990720, 185404290282527361386, 14389574562121084305408, 1221867855128546542385409, 108430221517525671050739712
Offset: 1

Views

Author

Seiichi Manyama, Nov 21 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sumdiv(n, d, (d+n)^n);

Formula

a(n) = Sum_{k=0..n} n^(n-k) * binomial(n,k) * sigma_k(n).

A367507 a(n) = Sum_{d|n} (d+2)^n.

Original entry on oeis.org

3, 25, 152, 1633, 17050, 282594, 4785156, 101751713, 2359920499, 62200947098, 1792160571184, 56765070083650, 1946195069953698, 72080471103601322, 2862427829603252768, 121449533922042173249, 5480386857784931326102, 262149577935595805876315
Offset: 1

Views

Author

Seiichi Manyama, Nov 21 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sumdiv(n, d, (d+2)^n);

Formula

a(n) = Sum_{k=0..n} 2^(n-k) * binomial(n,k) * sigma_k(n).

A367552 a(n) = Sum_{d|n} (d^2-1)^n.

Original entry on oeis.org

0, 9, 512, 50706, 7962624, 1838528498, 587068342272, 248158343164707, 134217728134217728, 90438270904261473426, 74300837068800000000000, 73119374851006048408704228, 84922087747184192618514874368, 114943537906488487820754156670578
Offset: 1

Views

Author

Seiichi Manyama, Nov 22 2023

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_]:= Sum[(-1)^(n-k)*Binomial[n,k]*DivisorSigma[2*k,n],{k,0,n}]; Array[a,14] (* Stefano Spezia, Nov 22 2023 *)
  • PARI
    a(n) = sumdiv(n, d, (d^2-1)^n);

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * sigma_{2*k}(n).
Showing 1-3 of 3 results.