This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A366967 #12 Oct 30 2023 13:11:12 %S A366967 0,1,4,11,21,40,61,96,135,191,246,337,415,528,646,801,937,1145,1316, %T A366967 1568,1802,2089,2342,2737,3047,3451,3841,4338,4744,5358,5823,6474, %U A366967 7060,7758,8384,9294,9960,10835,11657,12717,13537,14739,15642,16881,18025,19314,20395 %N A366967 a(n) = Sum_{k=2..n} binomial(k,2) * floor(n/k). %F A366967 G.f.: 1/(1-x) * Sum_{k>=1} x^(2*k)/(1-x^k)^3 = 1/(1-x) * Sum_{k>=2} binomial(k,2) * x^k/(1-x^k). %F A366967 a(n) = (A064602(n)-A024916(n))/2. - _Chai Wah Wu_, Oct 30 2023 %o A366967 (PARI) a(n) = sum(k=2, n, binomial(k, 2)*(n\k)); %o A366967 (Python) %o A366967 from math import isqrt %o A366967 def A366967(n): return ((s:=isqrt(n))**2*(1-s**2)+sum((q:=n//k)*(3*k*(k-1)+q**2-1) for k in range(1,s+1)))//6 # _Chai Wah Wu_, Oct 30 2023 %Y A366967 Partial sums of A069153. %Y A366967 Cf. A002541, A236632. %Y A366967 Cf. A024916, A064602, A366971. %K A366967 nonn %O A366967 1,3 %A A366967 _Seiichi Manyama_, Oct 30 2023