A253890 a(n) = A253560(A253883(n)) = A122111((2*A122111(n)) - 1).

1, 4, 16, 8, 18, 32, 2048, 9, 128, 512, 100, 256, 2147483648, 32768, 54, 64, 1200, 1024, 10616832, 144, 1048576, 864, 43200, 25, 65536, 8796093022208, 81, 4194304, 644972544, 131072, 7260, 36, 486, 75557863725914323419136, 268435456, 8192

Offset: 1

Author

Antti Karttunen, Jan 17 2015

Keywords

• nonn

Comments

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).

Thus after a(1)=1, this is a permutation of A070003 (numbers divisible by the square of their largest prime factor).

When A122111 is represented as a binary tree, then node A122111(t > 1) = n has as its left child A122111(2t-1) = a(n).

Crossrefs

Cf. A070003 (same sequence without 1, sorted into ascending order).

Cf. A005408, A122111, A253560, A253883.

Cf. also A112798 and A241918.

Formula

a(n) = A122111((2*A122111(n)) - 1) = A122111(A005408(A122111(n) - 1)).

a(n) = A253560(A253883(n)).