cp's OEIS Frontend

A366984 a(n) = Sum_{k=1..n} binomial(k+2,2) * floor(n/k).

%I A366984 #13 Oct 31 2023 19:14:57
%S A366984 3,12,25,49,73,120,159,228,296,392,473,626,734,899,1069,1291,1465,
%T A366984 1757,1970,2312,2614,2977,3280,3803,4178,4670,5144,5759,6227,6993,
%U A366984 7524,8307,8993,9803,10529,11630,12374,13373,14311,15559,16465,17867,18860,20273,21579,23016
%N A366984 a(n) = Sum_{k=1..n} binomial(k+2,2) * floor(n/k).
%F A366984 G.f.: 1/(1-x) * Sum_{k>0} (1/(1-x^k)^3 - 1) = 1/(1-x) * Sum_{k>0} binomial(k+2,2) * x^k/(1-x^k).
%o A366984 (PARI) a(n) = sum(k=1, n, binomial(k+2, 2)*(n\k));
%o A366984 (Python)
%o A366984 from math import isqrt
%o A366984 def A366984(n): return (-(s:=isqrt(n))*(s*(s*(s+7)+17)+17)+sum(((q:=n//w)+1)*(q*(q+5)+3*(w*(w+3)+4)) for w in range(1,s+1)))//6 # _Chai Wah Wu_, Oct 31 2023
%Y A366984 Partial sums of A363628.
%Y A366984 Cf. A006218, A366983, A366985.
%Y A366984 Cf. A366967.
%K A366984 nonn
%O A366984 1,1
%A A366984 _Seiichi Manyama_, Oct 30 2023