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 A365439 #17 Oct 27 2023 09:57:26 %S A365439 1,7,23,64,135,282,493,864,1375,2166,3168,4715,6536,9132,12278,16525, %T A365439 21371,27998,35314,44995,55847,69504,84455,103882,124428,150005, %U A365439 177921,212017,247978,292890,339267,395874,455796,526692,600788,691066,782457,891048,1004814 %N A365439 a(n) = Sum_{k=1..n} binomial(floor(n/k)+4,5). %F A365439 a(n) = Sum_{k=1..n} binomial(k+3,4) * floor(n/k). %F A365439 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). %F A365439 a(n) = (A064604(n)+6*A064603(n)+11*A064602(n)+6*A024916(n))/24. - _Chai Wah Wu_, Oct 26 2023 %o A365439 (PARI) a(n) = sum(k=1, n, binomial(n\k+4, 5)); %o A365439 (Python) %o A365439 from math import isqrt, comb %o A365439 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 %Y A365439 Partial sums of A073570. %Y A365439 Cf. A006218, A024916, A064602, A064603, A064604, A364970, A365409. %K A365439 nonn,easy %O A365439 1,2 %A A365439 _Seiichi Manyama_, Oct 23 2023