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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) = A026424(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) = A028260(1+a(k)).
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%I #24 Jul 28 2015 12:39:56

%S 1,2,4,3,7,6,10,5,9,12,11,16,15,24,18,8,17,14,22,20,26,19,29,25,28,36,

%T 35,55,39,44,31,13,30,27,21,38,34,51,46,42,37,57,40,47,32,52,45,62,56,

%U 50,68,60,82,81,67,121,86,93,105,72,65,79,33,59,64,23,53,48,41,58,49,85,71,77,66,111,99

%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) = A026424(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) = A028260(1+a(k)).

%C This shares with the permutation A122111 the property that each term of A244990 is mapped to a unique term of A028260 and each term of A244991 is mapped to a unique term of A026424.

%H Antti Karttunen, <a href="/A245614/b245614.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, a(n) = A026424(a(A244989(n))), otherwise a(n) = A028260(1+a(A244988(n)-1)).

%F As a composition of related permutations:

%F a(n) = A245604(A244321(n)).

%F For all n >= 1, A244992(n) = A066829(a(n)).

%o (Scheme, with memoization macro definec)

%o (definec (A245614 n) (cond ((= 1 n) 1) ((= 1 (A244992 n)) (A026424 (A245614 (A244989 n)))) (else (A028260 (+ 1 (A245614 (-1+ (A244988 n))))))))

%Y Inverse: A245613.

%Y Cf. A026424, A028260, A066829, A244988, A244989, A244990, A244991, A244992, A122111.

%Y Similar permutations: A244321, A244322, A245604, A227413, A237126, A243288, A243344, A243346, A245606.

%K nonn,look

%O 1,2

%A _Antti Karttunen_, Jul 27 2014