cp's OEIS Frontend

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

%I A366970 #15 Oct 30 2023 19:28:45
%S A366970 0,0,1,4,10,21,36,60,89,131,176,245,311,404,502,631,751,926,1079,1295,
%T A366970 1501,1756,1987,2330,2612,2978,3332,3779,4157,4707,5142,5736,6278,
%U A366970 6926,7508,8336,8966,9785,10555,11533,12313,13427,14288,15449,16521,17742,18777,20306
%N A366970 a(n) = Sum_{k=3..n} binomial(k-1,2) * floor(n/k).
%F A366970 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).
%F A366970 a(n) = (A064602(n)-3*A024916(n))/2 + A006218(n). - _Chai Wah Wu_, Oct 30 2023
%o A366970 (PARI) a(n) = sum(k=3, n, binomial(k-1, 2)*(n\k));
%o A366970 (Python)
%o A366970 from math import isqrt
%o A366970 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
%Y A366970 Partial sums of A363610.
%Y A366970 Cf. A006218, A024916, A064602, A366968, A366969, A366971.
%K A366970 nonn
%O A366970 1,4
%A A366970 _Seiichi Manyama_, Oct 30 2023