A366969 a(n) = Sum_{k=3..n} (k-2) * floor(n/k).

0, 0, 1, 3, 6, 11, 16, 24, 32, 43, 52, 69, 80, 97, 114, 136, 151, 179, 196, 227, 252, 281, 302, 347, 373, 408, 441, 486, 513, 570, 599, 651, 692, 739, 780, 854, 889, 942, 991, 1066, 1105, 1186, 1227, 1300, 1367, 1432, 1477, 1582, 1634, 1716, 1781, 1868, 1919, 2024

Offset: 1

Author

Seiichi Manyama, Oct 30 2023

Keywords

• nonn

Crossrefs

Partial sums of A152771.

Cf. A006218, A024916, A366968, A366970, A366971.

Programs

PARI

a(n) = sum(k=3, n, (k-2)*(n\k));

Python

from math import isqrt
def A366969(n): return n+(-(s:=isqrt(n))*(s*(s-2)-7)+sum(((q:=n//w)+1)*(q+(w<<1)-8) for w in range(1,s+1))>>1) # Chai Wah Wu, Oct 30 2023

Formula

G.f.: 1/(1-x) * Sum_{k>=1} x^(3*k)/(1-x^k)^2 = 1/(1-x) * Sum_{k>=3} (k-2) * x^k/(1-x^k).

a(n) = n + A024916(n) - 2*A006218(n). - Chai Wah Wu, Oct 30 2023