A366972 a(n) = Sum_{k=4..n} floor(n/k).

0, 0, 0, 1, 2, 3, 4, 6, 7, 9, 10, 13, 14, 16, 18, 21, 22, 25, 26, 30, 32, 34, 35, 40, 42, 44, 46, 50, 51, 56, 57, 61, 63, 65, 68, 74, 75, 77, 79, 85, 86, 91, 92, 96, 100, 102, 103, 110, 112, 116, 118, 122, 123, 128, 131, 137, 139, 141, 142, 151, 152, 154, 158, 163, 166

Offset: 1

Author

Seiichi Manyama, Oct 30 2023

Keywords

• nonn

Crossrefs

Column k=4 of A134867.

Partial sums of A321014.

Cf. A006218.

Programs

PARI

a(n) = sum(k=4, n, n\k);

Python

from math import isqrt
def A366972(n): return -(s:=isqrt(n))**2+(sum(n//k for k in range(4,s+1))<<1)+n+(n>>1)+n//3 if n>8 else (0,0,0,0,1,2,3,4,6)[n] # Chai Wah Wu, Oct 30 2023

Formula

G.f.: 1/(1-x) * Sum_{k>=1} x^(4*k)/(1-x^k) = 1/(1-x) * Sum_{k>=4} x^k/(1-x^k).

a(n) = A006218(n)-n-floor(n/2)-floor(n/3). - Chai Wah Wu, Oct 30 2023