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Self-inverse permutation of natural numbers: a(1) = 1; a(n) = A000079(A193231(A007814(n))) * A250469(a(A268674(n))).
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%I #7 Feb 11 2016 12:09:58

%S 1,2,3,8,5,6,7,4,21,10,11,24,13,14,15,32,17,42,19,40,9,22,23,12,55,26,

%T 27,56,29,30,31,16,69,34,35,168,37,38,39,20,41,18,43,88,93,46,47,96,

%U 91,110,123,104,53,54,25,28,117,58,59,120,61,62,63,64,65,138,67,136,33,70,71,84,73,74,75,152,77,78,79,160

%N Self-inverse permutation of natural numbers: a(1) = 1; a(n) = A000079(A193231(A007814(n))) * A250469(a(A268674(n))).

%H Antti Karttunen, <a href="/A268675/b268675.txt">Table of n, a(n) for n = 1..1914</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, a(n) = A000079(A193231(A007814(n))) * A250469(a(A268674(n))).

%F Other identities. For all n >= 1:

%F A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]

%F A020639(a(n)) = A020639(n). [More generally, it preserves the smallest prime dividing n.]

%F A055396(a(n)) = A055396(n).

%o (Scheme, with memoization-macro definec)

%o (definec (A268675 n) (if (= 1 n) 1 (* (A000079 (A193231 (A007814 n))) (A250469 (A268675 (A268674 n))))))

%Y Cf. A000079, A000265, A007814, A193231, A250469, A268674.

%Y Cf. also A268385.

%K nonn

%O 1,2

%A _Antti Karttunen_, Feb 11 2016