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%I #16 Jan 14 2015 16:15:27
%S 1,2,3,4,6,5,7,8,9,12,10,13,11,15,14,16,18,17,19,24,25,20,26,21,22,27,
%T 23,31,29,30,28,32,36,34,33,37,35,39,49,38,48,51,41,50,40,52,42,53,43,
%U 44,54,45,55,47,46,63,59,61,62,58,57,60,65,56,73,64,72,68,66,69
%N Permutation of natural numbers: a(1)=1; thereafter, if n is k-th number whose greatest prime factor has an odd index [i.e., n = A244991(k)], a(n) = 2*a(k), otherwise, when n is k-th number whose greatest prime factor has an even index [i.e., n = A244990(1+k)], a(n) = 1+(2*a(k)).
%H Antti Karttunen, <a href="/A244321/b244321.txt">Table of n, a(n) for n = 1..10001</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(1) = 1, and for n > 1, if A244992(n) = 1 [i.e. the greatest prime factor of n has an odd index], a(n) = 2 * A244321(A244989(n)), otherwise, a(n) = 1 + (2 * A244321(A244988(n)-1)).
%F For all n >= 1, A000035(a(n)) = 1 - A244992(n).
%o (Scheme, with memoization macro definec)
%o (definec (A244321 n) (cond ((= 1 n) 1) ((= 1 (A244992 n)) (* 2 (A244321 (A244989 n)))) (else (+ 1 (* 2 (A244321 (-1+ (A244988 n))))))))
%Y Inverse: A244322.
%Y Cf. A244988, A244989, A244990, A244991, A244992.
%Y Similar entanglement permutations: A135141, A237427, A243287, A243343, A243345.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jul 22 2014
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