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%I #23 Jan 09 2024 12:31:57
%S 1,2,4,3,8,6,5,16,9,7,11,10,32,18,13,12,17,15,22,20,35,19,66,14,24,21,
%T 34,25,23,33,31,45,63,37,27,26,41,36,29,43,69,40,134,30,47,39,44,68,
%U 71,50,38,46,67,131,28,49,42,70,64,52,92,48,127,65,61,75,55,51,89,83,73,60
%N Permutation of natural numbers: a(1) = 1; thereafter, if n is k-th number with an odd number of prime divisors (counted with multiplicity) [i.e., n = A026424(k)], a(n) = A244991(a(k)), otherwise, when n is k-th number > 1 with an even number of prime divisors [i.e., n = A028260(1+k)], a(n) = A244990(1+a(k)).
%C This shares with the permutation A122111 the property that each term of A028260 is mapped to a unique term of A244990 and each term of A026424 is mapped to a unique term of A244991.
%H Antti Karttunen, <a href="/A245613/b245613.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 A066829(n) = 1, a(n) = A244991(a(A055038(n))), otherwise a(n) = A244990(1+a(A055037(n)-1)).
%F As a composition of related permutations:
%F a(n) = A244322(A245603(n)).
%F For all n >= 1, A066829(n) = A244992(a(n)).
%o (Scheme, with memoization macro definec)
%o (definec (A245613 n) (cond ((= 1 n) 1) ((= 1 (A066829 n)) (A244991 (A245613 (A055038 n)))) (else (A244990 (+ 1 (A245613 (-1+ (A055037 n))))))))
%Y Inverse: A245614.
%Y Cf. A026424, A028260, A055037, A055038, A066829, A244990, A244991, A244992, A122111.
%Y Similar entanglement permutations: A243287, A243343, A243345, A244321-A244322, A245603, A135141, A237427, A245605.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jul 27 2014
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