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).

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%I A344128 #8 May 14 2021 09:14:38
%S A344128 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,
%T A344128 53,57,60,61,62,63,70,71,72,73,85,86,87,88,91,92,93,94,97,101,102,103,
%U A344128 110,118,124,125,128,129,133,134,137,138,139,140,143,144,145,149,164,165,166
%N A344128 a(n) = Sum_{k=1..n} k * floor(n/k^2).
%F A344128 G.f.: (1/(1 - x)) * Sum_{k>=1} k * x^(k^2) / (1 - x^(k^2)). - _Ilya Gutkovskiy_, May 14 2021
%p A344128 b:= n-> mul((i[1]^(iquo(i[2], 2)+1)-1)/(i[1]-1), i=ifactors(n)[2]):
%p A344128 a:= proc(n) a(n):= a(n-1)+b(n) end: a(0):=0:
%p A344128 seq(a(n), n=1..66);  # _Alois P. Heinz_, May 14 2021
%t A344128 Table[Sum[k*Floor[n/k^2], {k, n}], {n, 100}]
%Y A344128 Partial sums of A069290.
%Y A344128 Cf. A013936.
%K A344128 nonn
%O A344128 1,2
%A A344128 _Wesley Ivan Hurt_, May 09 2021