A366970 a(n) = Sum_{k=3..n} binomial(k-1,2) * floor(n/k).

0, 0, 1, 4, 10, 21, 36, 60, 89, 131, 176, 245, 311, 404, 502, 631, 751, 926, 1079, 1295, 1501, 1756, 1987, 2330, 2612, 2978, 3332, 3779, 4157, 4707, 5142, 5736, 6278, 6926, 7508, 8336, 8966, 9785, 10555, 11533, 12313, 13427, 14288, 15449, 16521, 17742, 18777, 20306

Offset: 1

Author

Seiichi Manyama, Oct 30 2023

Keywords

• nonn

Crossrefs

Partial sums of A363610.

Cf. A006218, A024916, A064602, A366968, A366969, A366971.

Programs

PARI

a(n) = sum(k=3, n, binomial(k-1, 2)*(n\k));

Python

from math import isqrt
def A366970(n): return (-(s:=isqrt(n))*(s*(s**2-(s<<1)-1)+8)+sum(((q:=n//w)+1)*(q*(q-4)+3*(w**2-3*w+4)) for w in range(1,s+1)))//6 # Chai Wah Wu, Oct 30 2023

Formula

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

a(n) = (A064602(n)-3*A024916(n))/2 + A006218(n). - Chai Wah Wu, Oct 30 2023