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 A360303 #22 Feb 18 2023 21:18:44
%S A360303 0,1,2,4,9,17,34,66,132,261,521,1033,2066,4114,8226,16420,32837,65605,
%T A360303 131209,262281,524554,1048850,2097682,4194834,8389668,16778277,
%U A360303 33556517,67110981,134221897,268439625,536879242,1073750154,2147500178,4294983954,8589967634,17179902228,34359804453
%N A360303 a(n) = Sum_{k=1..floor(sqrt(n))} 2^floor(n/k-k).
%C A360303 This sequence corresponds to the left half of a drawing, the whole drawing being reconstituted by symmetry (see the Illustration link). The divisors of n are closely related to the occurrences of the bit pattern "01 over 10" in the 2 X 2 squares along the (n-1)th and n-th lines (see the pattern link). In particular, n is a prime number if and only if a(n) - a(n-1) = 2^(n-2).
%H A360303 Luc Rousseau, <a href="/A360303/a360303.svg">Illustration in black and white, n = 0..100</a>.
%H A360303 Luc Rousseau, <a href="/A360303/a360303_1.svg">Illustrated bit pattern for the detection of divisors, n = 1..9</a>.
%F A360303 a(n) = Sum_{k=1..floor(sqrt(n))} 2^floor(n/k - k).
%e A360303 For n = 5, floor(sqrt(n)) = 2. So, two bits are set in a(n); they are the bits number floor(5/1-1)=4 and floor(5/2-2)=0, so a(n) = 10001_2 = 17.
%o A360303 (PARI)
%o A360303 a(n)=sum(k=1,floor(sqrt(n)),2^floor(n/k-k))
%Y A360303 Cf. A034729.
%K A360303 nonn,base
%O A360303 0,3
%A A360303 _Luc Rousseau_, Feb 02 2023