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 A359503 #33 Jan 26 2024 06:56:08
%S A359503 1,2,3,6,7,10,11,14,18,21,22,28,29,32,36,43,44,50,51,58,62,65,66,76,
%T A359503 82,85,89,96,97,108,109,116,120,123,129,145,146,149,153,165,166,178,
%U A359503 179,186,195,198,199,215,223,231,235,242,243,255,261,275,279,282,283
%N A359503 Partial sums of A066839.
%C A359503 a(n) is the sum of all divisors d of k such that d^2 <= k where k ranges from 1 to n.
%F A359503 a(n) = m*(6*n+5-m*(2*m+3))/6 + Sum_{k=1..n, i=1..floor(sqrt(k))} [(k-1) mod i] - [k mod i] where m = floor(sqrt(n)).
%F A359503 a(n) = m*(6*n+5-m*(2*m+3))/6 + Sum_{k=1..n, i=1..floor(sqrt(k))} (k-1) mod i - Sum_{k=1..n} A176314(k) where m = floor(sqrt(n)).
%t A359503 Table[Select[Divisors[n], # <= Sqrt[n]&]//Total, {n, 1, 60}]//Accumulate (* _Jean-François Alcover_, Jan 26 2024 *)
%o A359503 (Python)
%o A359503 from itertools import takewhile
%o A359503 from sympy import divisors
%o A359503 def A359503(n): return sum(sum(takewhile(lambda x:x**2<=i,divisors(i))) for i in range(1,n+1))
%Y A359503 Cf. A066839, A176314.
%K A359503 nonn
%O A359503 1,2
%A A359503 _Chai Wah Wu_, Jan 24 2024