A049792 a(n) = Sum_{k=1..n} floor(n/floor(n/k)).

1, 3, 7, 11, 18, 24, 34, 43, 55, 66, 82, 94, 113, 129, 150, 167, 192, 211, 239, 261, 290, 315, 349, 374, 410, 440, 478, 509, 552, 583, 629, 665, 711, 750, 802, 838, 893, 937, 992, 1036, 1097, 1141, 1205, 1255, 1317, 1370, 1440

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A049790, A049791, A049793, A049794, A049795, A049796.

Programs

GAP

List([1..60], n-> Sum([1..n], j-> Int(n/Int(n/j)) )); # G. C. Greubel, Dec 10 2019

Magma

[(&+[Floor(n/Floor(n/j)): j in [1..n]]): n in [1..60]]; // G. C. Greubel, Dec 10 2019

Maple

seq( add(floor(n/floor(n/j)), j=1..n), n=1..60); # G. C. Greubel, Dec 10 2019

Mathematica

Table[Total[Table[Quotient[n, Quotient[n, k]], {k, n}]], {n, 47}] (* Ivan Neretin, Jul 29 2015 *)

PARI

a(n) = sum(j=1,n, n\(n\j));
vector(60, n, a(n) ) \\ G. C. Greubel, Dec 10 2019

Sage

[sum(floor(n/floor(n/j)) for j in (1..n)) for n in (1..60)] # G. C. Greubel, Dec 10 2019

Formula

a(n) = A049790(n, n).

a(n) = A222548(n) - Sum_{i=1..n} floor(n/i)*floor(n/(i+1)). - Ridouane Oudra, Jun 22 2020

a(n) ~ (zeta(2) - 1) * n^2. - Vaclav Kotesovec, May 28 2021