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A365439
a(n) = Sum_{k=1..n} binomial(floor(n/k)+4,5).
6
1, 7, 23, 64, 135, 282, 493, 864, 1375, 2166, 3168, 4715, 6536, 9132, 12278, 16525, 21371, 27998, 35314, 44995, 55847, 69504, 84455, 103882, 124428, 150005, 177921, 212017, 247978, 292890, 339267, 395874, 455796, 526692, 600788, 691066, 782457, 891048, 1004814
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).
a(n) = (A064604(n)+6*A064603(n)+11*A064602(n)+6*A024916(n))/24. - Chai Wah Wu, Oct 26 2023
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
Partial sums of A073570.
Sequence in context: A003261 A306971 A343519 * A266801 A066187 A259214
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Oct 23 2023
STATUS
approved