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%I #19 Aug 13 2017 21:27:49
%S 1,4,16,8,18,32,2048,9,128,512,100,256,2147483648,32768,54,64,1200,
%T 1024,10616832,144,1048576,864,43200,25,65536,8796093022208,81,
%U 4194304,644972544,131072,7260,36,486,75557863725914323419136,268435456,8192
%N a(n) = A253560(A253883(n)) = A122111((2*A122111(n)) - 1).
%C Conjugate the partition defined by the prime factorization of n (see, e.g., table A112798 or A241918), resulting k = A122111(n), then take the k-th odd number (2k-1), and conjugate again, giving a(n) = A122111(2k-1).
%C Thus after a(1)=1, this is a permutation of A070003 (numbers divisible by the square of their largest prime factor).
%C When A122111 is represented as a binary tree, then node A122111(t > 1) = n has as its left child A122111(2t-1) = a(n).
%F a(n) = A122111((2*A122111(n)) - 1) = A122111(A005408(A122111(n) - 1)).
%F a(n) = A253560(A253883(n)).
%o (Scheme, two alternative definitions)
%o (define (A253890 n) (A253560 (A253883 n)))
%o (define (A253890 n) (A122111 (- (* 2 (A122111 n)) 1)))
%Y Cf. A070003 (same sequence without 1, sorted into ascending order).
%Y Cf. A005408, A122111, A253560, A253883.
%Y Cf. also A112798 and A241918.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jan 17 2015
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