Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Jun 11 2020 23:44:04
%S 1,2,4,3,16,8,9,6,256,32,64,12,81,18,36,5,65536,512,1024,48,4096,128,
%T 144,24,6561,162,324,27,1296,72,25,10,4294967296,131072,262144,768,
%U 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 a(0) = 1, and then after, a(2n) = a(n)^2, a(2n+1) = A334747(a(n)).
%C 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 1
%C |
%C ...................2...................
%C 4 3
%C 16......../ \........8 9......../ \........6
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C 256 32 64 12 81 18 36 5
%C 65536 512 1024 48 4096 128 144 24 6561 162 324 27 1296 72 25 10
%C etc.
%C This is the mirror image of the tree in A334860.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(0) = 1, and then after, a(2n) = a(n)^2, a(2n+1) = A334747(a(n)).
%F a(n) = A225546(A005940(1+n)).
%F For all n >= 0, A048675(a(n)) = A087808(n).
%o (PARI)
%o A334747(n) = { my(c=core(n), m=n); forprime(p=2, , if(c % p, m*=p; break, m/=p)); m; }; \\ From A334747
%o A334866(n) = if(!n,1,if(!(n%2),A334866(n/2)^2,A334747(A334866((n-1)/2))));
%Y Cf. A334865 (inverse permutation), A334860 (mirror image).
%Y Composition of permutations A005940 and A225546.
%Y Cf. A000290, A048675, A087808, A334747, A334870.
%Y Cf. A001146 (left edge of the tree), A019565 (right edge), A334110 (the left children of the right edge).
%K nonn,tabf
%O 0,2
%A _Antti Karttunen_, Jun 08 2020