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 A253890 #19 Aug 13 2017 21:27:49 %S A253890 1,4,16,8,18,32,2048,9,128,512,100,256,2147483648,32768,54,64,1200, %T A253890 1024,10616832,144,1048576,864,43200,25,65536,8796093022208,81, %U A253890 4194304,644972544,131072,7260,36,486,75557863725914323419136,268435456,8192 %N A253890 a(n) = A253560(A253883(n)) = A122111((2*A122111(n)) - 1). %C A253890 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 A253890 Thus after a(1)=1, this is a permutation of A070003 (numbers divisible by the square of their largest prime factor). %C A253890 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 A253890 a(n) = A122111((2*A122111(n)) - 1) = A122111(A005408(A122111(n) - 1)). %F A253890 a(n) = A253560(A253883(n)). %o A253890 (Scheme, two alternative definitions) %o A253890 (define (A253890 n) (A253560 (A253883 n))) %o A253890 (define (A253890 n) (A122111 (- (* 2 (A122111 n)) 1))) %Y A253890 Cf. A070003 (same sequence without 1, sorted into ascending order). %Y A253890 Cf. A005408, A122111, A253560, A253883. %Y A253890 Cf. also A112798 and A241918. %K A253890 nonn %O A253890 1,2 %A A253890 _Antti Karttunen_, Jan 17 2015