OFFSET
1,2
FORMULA
a(n) = Sum_{k=1..n} binomial(k+3,4) * floor(n/k).
G.f.: 1/(1-x) * Sum_{k>=1} x^k/(1-x^k)^5 = 1/(1-x) * Sum_{k>=1} binomial(k+3,4) * x^k/(1-x^k).
PROG
(PARI) a(n) = sum(k=1, n, binomial(n\k+4, 5));
(Python)
from math import isqrt, comb
def A365439(n): return (-(s:=isqrt(n))**2*comb(s+4, 4)+sum((q:=n//k)*(5*comb(k+3, 4)+comb(q+4, 4)) for k in range(1, s+1)))//5 # Chai Wah Wu, Oct 26 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Oct 23 2023
STATUS
approved