A366968 a(n) = Sum_{k=3..n} floor(n/k).

0, 0, 1, 2, 3, 5, 6, 8, 10, 12, 13, 17, 18, 20, 23, 26, 27, 31, 32, 36, 39, 41, 42, 48, 50, 52, 55, 59, 60, 66, 67, 71, 74, 76, 79, 86, 87, 89, 92, 98, 99, 105, 106, 110, 115, 117, 118, 126, 128, 132, 135, 139, 140, 146, 149, 155, 158, 160, 161, 171, 172, 174, 179, 184

Offset: 1

Author

Seiichi Manyama, Oct 30 2023

Keywords

• nonn
• easy

Crossrefs

Column k=3 of A134867.

Partial sums of A023645.

Cf. A006218, A366969, A366970, A366971.

Programs

PARI

a(n) = sum(k=3, n, n\k);

Python

from math import isqrt
def A366968(n): return -(s:=isqrt(n))**2+(sum(n//k for k in range(3,s+1))<<1)+n+(n>>1) if n>3 else int(n>2) # Chai Wah Wu, Oct 30 2023

Formula

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

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