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 A363537 #6 Jun 11 2023 12:29:33
%S A363537 0,1,2,4,3,8,5,16,9,32,6,17,64,10,33,128,18,7,65,12,256,34,11,129,20,
%T A363537 512,66,19,257,36,1024,13,130,24,35,513,68,2048,21,258,40,67,1025,132,
%U A363537 4096,37,514,72,14,131,2049,25,260,48,8192,69,1026,136,22,259,4097,41,516,80,16384,133,2050,264,38
%N A363537 Rewrite A087980(n) = Product_{i=1..m} p(i)^e(i) instead as Sum_{i=1..m} 2^(i-1), where m = omega(A087980(n)) = A001221(A087980(n)).
%C A363537 Permutation of nonnegative numbers.
%C A363537 Rewriting nonnegative numbers n = Sum_{i=1..A000120(n)} 2^i instead as Product_{i=1..A000120(n)} p(i)^(e(i)+1) gives A362227.
%H A363537 Michael De Vlieger, <a href="/A363537/b363537.txt">Table of n, a(n) for n = 1..11157</a> (a(11157) = 2^64.)
%H A363537 Michael De Vlieger, <a href="/A363537/a363537.png">Log log scatterplot of a(n)</a>, n = 1..1203278.
%H A363537 Michael De Vlieger, <a href="/A363537/a363537_1.png">Plot S(n,k) in row a(n) of A272011 at (x,y) = (n,k)</a>, n = 1..2048.
%F A363537 a(2^k) = 2^(k-1) for k > 0.
%F A363537 a(A006939(k)) = 2^k-1 for k > 0.
%e A363537 Table relating this sequence to A087980, where b(n) = A087980(n), f(n) = A067255(n), g(n) = A272011(n), and a(n)_2 the binary expansion of a(n):
%e A363537 n b(n) f(b(n)) a(n) g(a(n)) a(n)_2
%e A363537 1 1 0 0
%e A363537 2 2 1 1 0 1
%e A363537 3 4 2 2 1 1.
%e A363537 4 8 3 4 2 1..
%e A363537 5 12 2,1 3 1,0 11
%e A363537 6 16 4 8 3 1...
%e A363537 7 24 3,1 5 2,0 1.1
%e A363537 8 32 5 16 4 1....
%e A363537 9 48 4,1 9 3,0 1..1
%e A363537 10 64 6 32 5 1.....
%e A363537 11 72 3,2 6 2,1 11.
%e A363537 12 96 5,1 17 4,0 1...1
%e A363537 13 128 7 64 6 1......
%e A363537 14 144 4,2 10 3,1 1.1.
%e A363537 15 192 6,1 33 5,0 1....1
%e A363537 16 256 8 128 7 1.......
%e A363537 17 288 5,2 18 4,1 1..1.
%e A363537 18 360 3,2,1 7 2,1,0 111
%e A363537 ...
%t A363537 m = 15; f[n_] := Times @@ MapIndexed[Prime[First[#2]]^(#1 + 1) &, Length[#] - Position[#, 1][[All, 1]]] &[IntegerDigits[n, 2]]; SortBy[Select[Array[{#, f[#]} &, 2^(m + 1)], Last[#] <= 2^m &], Last][[All, 1]]
%Y A363537 Cf. A000079, A001221, A006939, A087980, A362227.
%K A363537 nonn
%O A363537 1,3
%A A363537 _Michael De Vlieger_, Jun 09 2023