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

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

1,2

Links

Table of n, a(n) for n=1..66.

Formula

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

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}]

Crossrefs

Partial sums of A069290.

Cf. A013936.

Sequence in context: A102806 A275884 A003605 * A132188 A326027 A255527

Adjacent sequences: A344125 A344126 A344127 * A344129 A344130 A344131

Keyword

nonn

Author

Wesley Ivan Hurt, May 09 2021

Status

approved