A366985 a(n) = Sum_{k=1..n} binomial(k+3,3) * floor(n/k).

4, 18, 42, 91, 151, 269, 393, 607, 851, 1207, 1575, 2183, 2747, 3561, 4457, 5640, 6784, 8452, 9996, 12158, 14326, 17004, 19608, 23306, 26642, 30870, 35174, 40518, 45482, 52214, 58202, 65930, 73458, 82382, 90998, 102295, 112179, 124393, 136457, 151125, 164373

Offset: 1

Author

Seiichi Manyama, Oct 30 2023

Keywords

• nonn

Crossrefs

Partial sums of A116963.

Cf. A006218, A366983, A366984.

Cf. A366971.

Programs

PARI

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

Python

from math import isqrt
def A366985(n): return (-(s:=isqrt(n))*(s*(s*(s*(s+11)+45)+85)+74)+sum(((q:=n//w)+1)*(q*(q*(q+9)+26)+((w+4)*(w*(w+2)+3)<<2)) for w in range(1,s+1)))//3>>3 # Chai Wah Wu, Oct 31 2023

Formula

G.f.: 1/(1-x) * Sum_{k>0} (1/(1-x^k)^4 - 1) = 1/(1-x) * Sum_{k>0} binomial(k+3,3) * x^k/(1-x^k).