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 A334866 #10 Jun 11 2020 23:44:04
%S A334866 1,2,4,3,16,8,9,6,256,32,64,12,81,18,36,5,65536,512,1024,48,4096,128,
%T A334866 144,24,6561,162,324,27,1296,72,25,10,4294967296,131072,262144,768,
%U A334866 1048576,2048,2304,96,16777216,8192,16384,192,20736,288,576,20,43046721,13122,26244,243,104976,648,729,54,1679616,2592,5184,108,625,50,100,15
%N A334866 a(0) = 1, and then after, a(2n) = a(n)^2, a(2n+1) = A334747(a(n)).
%C A334866 This irregular table can be represented as a binary tree. Each child to the left is obtained by squaring the parent, and each child to the right is obtained by applying A334747 to the parent:
%C A334866 1
%C A334866 |
%C A334866 ...................2...................
%C A334866 4 3
%C A334866 16......../ \........8 9......../ \........6
%C A334866 / \ / \ / \ / \
%C A334866 / \ / \ / \ / \
%C A334866 / \ / \ / \ / \
%C A334866 256 32 64 12 81 18 36 5
%C A334866 65536 512 1024 48 4096 128 144 24 6561 162 324 27 1296 72 25 10
%C A334866 etc.
%C A334866 This is the mirror image of the tree in A334860.
%H A334866 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A334866 a(0) = 1, and then after, a(2n) = a(n)^2, a(2n+1) = A334747(a(n)).
%F A334866 a(n) = A225546(A005940(1+n)).
%F A334866 For all n >= 0, A048675(a(n)) = A087808(n).
%o A334866 (PARI)
%o A334866 A334747(n) = { my(c=core(n), m=n); forprime(p=2, , if(c % p, m*=p; break, m/=p)); m; }; \\ From A334747
%o A334866 A334866(n) = if(!n,1,if(!(n%2),A334866(n/2)^2,A334747(A334866((n-1)/2))));
%Y A334866 Cf. A334865 (inverse permutation), A334860 (mirror image).
%Y A334866 Composition of permutations A005940 and A225546.
%Y A334866 Cf. A000290, A048675, A087808, A334747, A334870.
%Y A334866 Cf. A001146 (left edge of the tree), A019565 (right edge), A334110 (the left children of the right edge).
%K A334866 nonn,tabf
%O A334866 0,2
%A A334866 _Antti Karttunen_, Jun 08 2020