A351620 a(1) = 1; a(n) = a(n-1) + Sum_{k=2..n} a(floor(n/k)).

1, 2, 4, 8, 13, 22, 32, 48, 67, 93, 120, 164, 209, 266, 331, 418, 506, 626, 747, 905, 1076, 1276, 1477, 1755, 2039, 2370, 2723, 3149, 3576, 4112, 4649, 5295, 5971, 6737, 7519, 8501, 9484, 10590, 11744, 13109, 14475, 16092, 17710, 19561, 21504, 23650, 25797, 28386, 30986, 33903

Offset

1,2

Comments

Partial sums of A320225.

Links

Table of n, a(n) for n=1..50.

Formula

G.f. A(x) satisfies: A(x) = x/(1 - x) + (1/(1 - x)^2) * Sum_{k>=2} (1 - x^k) * A(x^k).

Mathematica

a[1] = 1; a[n_] := a[n] = a[n - 1] + Sum[a[Floor[n/k]], {k, 2, n}]; Table[a[n], {n, 1, 50}]

Crossrefs

Cf. A001519, A022825, A025523, A033485, A078346, A320225, A351621.

Sequence in context: A164431 A164480 A134035 * A078157 A144119 A207033

Adjacent sequences: A351617 A351618 A351619 * A351621 A351622 A351623

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 20 2022

Status

approved