A366983 a(n) = Sum_{k=1..n} (k+1) * floor(n/k).

2, 7, 13, 23, 31, 47, 57, 76, 92, 114, 128, 162, 178, 206, 234, 270, 290, 335, 357, 405, 441, 481, 507, 575, 609, 655, 699, 761, 793, 873, 907, 976, 1028, 1086, 1138, 1238, 1278, 1342, 1402, 1500, 1544, 1648, 1694, 1784, 1868, 1944, 1994, 2128, 2188, 2287, 2363, 2467

Offset: 1

Author

Seiichi Manyama, Oct 30 2023

Keywords

• nonn
• easy

Crossrefs

Partial sums of A007503.

Cf. A006218, A366984, A366985.

Cf. A024916, A257644.

Programs

PARI

a(n) = sum(k=1, n, (k+1)*(n\k));

Python

from math import isqrt
def A366983(n): return -(s:=isqrt(n))*(s*(s+4)+5)+sum(((q:=n//w)+1)*(q+(w<<1)+4) for w in range(1,s+1))>>1 # Chai Wah Wu, Oct 31 2023

Formula

a(n) = A006218(n) + A024916(n).

G.f.: 1/(1-x) * Sum_{k>0} (1/(1-x^k)^2 - 1) = 1/(1-x) * Sum_{k>0} (k+1) * x^k/(1-x^k).

a(n) = A257644(n) - 1. - Hugo Pfoertner, Oct 31 2023