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