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 A362227 #30 Jun 11 2023 12:29:09
%S A362227 1,2,4,12,8,24,72,360,16,48,144,720,432,2160,10800,75600,32,96,288,
%T A362227 1440,864,4320,21600,151200,2592,12960,64800,453600,324000,2268000,
%U A362227 15876000,174636000,64,192,576,2880,1728,8640,43200,302400,5184,25920,129600,907200,648000,4536000,31752000,349272000,15552
%N A362227 a(n) = Product_{k=1..w(n)} p(k)^(S(n,k)-1), where set S(n,k) = row n of A272011 and w(n) = A000120(n) is the binary weight of n.
%C A362227 In other words, let S(n) contain place values of 1's in the binary expansion of n, ordered greatest to least, where S(n,1) = floor(log_2(n+1)) = A000523(n+1) and the remaining terms in S strictly decrease. This sequence reads S(n,k)+1 instead as a multiplicity of prime(k) so as to produce a number with strictly decreasing prime exponents.
%H A362227 Michael De Vlieger, <a href="/A362227/b362227.txt">Table of n, a(n) for n = 0..16384</a>
%F A362227 This sequence, sorted, is A087980.
%F A362227 a(2^k) = 2^(k+1).
%F A362227 a(2^k-1) = A006939(k-1).
%e A362227 a(0) = 1 since 1 is the empty product.
%e A362227 a(1) = 2 since 1 = 2^0, s = {0}, hence a(1) = prime(1)^(0+1) = 2^1 = 2.
%e A362227 a(2) = 4 since 2 = 2^1, s = {1}, hence a(2) = 2^(1+1) = 4.
%e A362227 a(3) = 12 since 3 = 2^1+2^0, s = {1,0}, hence a(3) = 2^2*3^1 = 12, etc.
%e A362227 The table below relates first terms of this sequence greater than 1 to A272011 and A067255:
%e A362227 n A272011(n) a(n) A067255(a(n))
%e A362227 ------------------------------------
%e A362227 1 0 2 1
%e A362227 2 1 4 2
%e A362227 3 1,0 12 2,1
%e A362227 4 2 8 3
%e A362227 5 2,0 24 3,1
%e A362227 6 2,1 72 3,2
%e A362227 7 2,1,0 360 3,2,1
%e A362227 8 3 16 4
%e A362227 9 3,0 48 4,1
%e A362227 10 3,1 144 4,2
%e A362227 11 3,1,0 720 4,2,1
%e A362227 12 3,2 432 4,3
%e A362227 13 3,2,0 2160 4,3,1
%e A362227 14 3,2,1 10800 4,3,2
%e A362227 15 3,2,1,0 75600 4,3,2,1
%e A362227 16 4 32 5
%e A362227 ...
%e A362227 This sequence appears below, seen as an irregular triangle T(m,j) delimited by 2^m where j = 1..2^(m-1) for m > 0:
%e A362227 1;
%e A362227 2;
%e A362227 4, 12;
%e A362227 8, 24, 72, 360;
%e A362227 16, 48, 144, 720, 432, 2160, 10800, 75600;
%e A362227 ...
%e A362227 T(m,1) = 2^m.
%e A362227 T(m,2^(m-1)) = A006939(m) for m > 0.
%t A362227 Array[Times @@ MapIndexed[Prime[First[#2]]^(#1 + 1) &, Length[#] - Position[#, 1][[All, 1]] ] &[IntegerDigits[#, 2]] &, 48, 0]
%Y A362227 Cf. A000120, A006939, A067255, A087980, A272011.
%K A362227 nonn,easy
%O A362227 0,2
%A A362227 _Michael De Vlieger_, Jun 08 2023