A253890 - OEIS

%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