A243287 - OEIS

%I #28 Jan 21 2020 02:33:17

%S 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,

%T 72,33,96,256,28,80,11,68,26,144,19,66,192,512,56,160,22,136,52,288,

%U 38,132,384,25,65,1024,112,320,21,44,272,104,576,76,264,768,50,130,37,2048

%N 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).

%C 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).

%C 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.

%H Antti Karttunen, <a href="/A243287/b243287.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F 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).

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (definec (A243287 n) (cond ((<= n 1) n) ((zero? (A241917 n)) (+ 1 (* 2 (A243287 (A243282 n))))) (else (* 2 (A243287 (A243285 n))))))

%Y Inverse: A243288.

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

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

%K nonn,look

%O 1,2

%A _Antti Karttunen_, Jun 02 2014