A024917 a(n) = Sum_{k=2..n} k*floor(n/k).

2, 5, 11, 16, 27, 34, 48, 60, 77, 88, 115, 128, 151, 174, 204, 221, 259, 278, 319, 350, 385, 408, 467, 497, 538, 577, 632, 661, 732, 763, 825, 872, 925, 972, 1062, 1099, 1158, 1213, 1302, 1343, 1438, 1481, 1564, 1641, 1712, 1759, 1882, 1938, 2030, 2101, 2198, 2251

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Cf. A002541, A024916, A345682.

Programs

Magma

[&+[k*Floor(n/k): k in [2..n]]: n in [2..55]]; // Bruno Berselli, Jan 08 2012

Mathematica

Table[Sum[k*Floor[n/k],{k,2,n}],{n,2,60}] (* Harvey P. Dale, Mar 13 2015 *)

PARI

a(n) = sum(k=2,n, k*floor(n/k)); \\ Michel Marcus, Sep 02 2019

Python

from math import isqrt
def A024917(n): return (-(s:=isqrt(n))**2*(s+1)+sum((q:=n//k)*((k<<1)+q+1) for k in range(1,s+1))>>1)-n # Chai Wah Wu, Oct 23 2023

Formula

G.f.: (1/(1 - x)) * Sum_{k>=2} k*x^k/(1 - x^k). - Ilya Gutkovskiy, Sep 02 2019