A351621 a(1) = 1; a(n) = 1 + a(n-1) + Sum_{k=2..n} a(floor(n/k)).

1, 3, 6, 12, 19, 32, 46, 69, 96, 133, 171, 234, 298, 379, 471, 595, 720, 891, 1063, 1288, 1531, 1815, 2100, 2496, 2900, 3371, 3873, 4479, 5086, 5848, 6611, 7530, 8491, 9580, 10691, 12088, 13486, 15059, 16700, 18642, 20585, 22885, 25186, 27818, 30580, 33630, 36681, 40363, 44060, 48208

Offset: 1

Author

Ilya Gutkovskiy, Feb 20 2022

Keywords

• nonn

Comments

Partial sums of A345139.

Crossrefs

Cf. A001906, A022825, A025523, A078346, A102378, A345139, A351620.

Programs

Mathematica

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

Formula

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