A243287 a(1)=1, and for n > 1, if n is k-th number divisible by the square of its largest prime factor (i.e., n = A070003(k)), a(n) = 1 + (2*a(k)); otherwise, when n = A102750(k), a(n) = 2*a(k).

1, 2, 4, 3, 8, 6, 16, 5, 9, 12, 32, 10, 18, 24, 64, 7, 20, 17, 36, 48, 128, 14, 40, 34, 13, 72, 33, 96, 256, 28, 80, 11, 68, 26, 144, 19, 66, 192, 512, 56, 160, 22, 136, 52, 288, 38, 132, 384, 25, 65, 1024, 112, 320, 21, 44, 272, 104, 576, 76, 264, 768, 50, 130, 37, 2048

Offset

1,2

Comments

This is an instance of "entanglement permutation", where two pairs of complementary subsets of natural numbers are interwoven with each other. In this case complementary pair A070003/A102750 (numbers which are divisible/not divisible by the square of their largest prime factor) is entangled with complementary pair odd/even numbers (A005408/A005843).

Thus this shares with the permutation A122111 the property that each term of A102750 is mapped to a unique even number and likewise each term of A070003 is mapped to a unique odd number.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, and thereafter, if A241917(n) = 0 (i.e., n is a term of A070003), a(n) = 1 + (2*a(A243282(n))); otherwise a(n) = 2*a(A243285(n)) (where A243282 and A243285 give the number of integers <= n divisible/not divisible by the square of their largest prime factor).

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(definec (A243287 n) (cond ((<= n 1) n) ((zero? (A241917 n)) (+ 1 (* 2 (A243287 (A243282 n))))) (else (* 2 (A243287 (A243285 n))))))

Crossrefs

Inverse: A243288.

Cf. A005843, A005408, A070003, A102750, A243282, A243285, A241917, A122111.

Similarly constructed permutations: A243343-A243346, A135141-A227413, A237126-A237427, A193231.

Sequence in context: A243073 A243345 A297499 * A243288 A279352 A279351

Adjacent sequences: A243284 A243285 A243286 * A243288 A243289 A243290

Keyword

nonn,look

Author

Antti Karttunen, Jun 02 2014

Status

approved