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.

A344128 a(n) = Sum_{k=1..n} k * floor(n/k^2).

Original entry on oeis.org

1, 2, 3, 6, 7, 8, 9, 12, 16, 17, 18, 21, 22, 23, 24, 31, 32, 36, 37, 40, 41, 42, 43, 46, 52, 53, 57, 60, 61, 62, 63, 70, 71, 72, 73, 85, 86, 87, 88, 91, 92, 93, 94, 97, 101, 102, 103, 110, 118, 124, 125, 128, 129, 133, 134, 137, 138, 139, 140, 143, 144, 145, 149, 164, 165, 166
Offset: 1

Views

Author

Wesley Ivan Hurt, May 09 2021

Keywords

Crossrefs

Partial sums of A069290.
Cf. A013936.

Programs

  • Maple
    b:= n-> mul((i[1]^(iquo(i[2], 2)+1)-1)/(i[1]-1), i=ifactors(n)[2]):
    a:= proc(n) a(n):= a(n-1)+b(n) end: a(0):=0:
    seq(a(n), n=1..66);  # Alois P. Heinz, May 14 2021
  • Mathematica
    Table[Sum[k*Floor[n/k^2], {k, n}], {n, 100}]

Formula

G.f.: (1/(1 - x)) * Sum_{k>=1} k * x^(k^2) / (1 - x^(k^2)). - Ilya Gutkovskiy, May 14 2021