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%I #17 Sep 29 2023 20:23:37
%S 1,4,6,2,10,9,14,12,3,15,22,8,26,21,20,18,34,16,38,25,28,33,46,27,5,
%T 39,30,35,58,24,62,36,44,51,42,32,74,57,52,45,82,49,86,55,50,69,94,54,
%U 7,60,68,65,106,48,66,63,76,87,118,70,122,93,77,72,78,88
%N Lexicographically earliest sequence of distinct terms, with a unique fixed point, such that a^n(n)=n, for any n>0 (where a^n denotes the n-th iterate of a).
%C The unique fixed point constraint ensures that this sequence differs from A000027.
%C This is a permutation of the natural numbers, with inverse A256513.
%C The length of the orbit of n is a prime divisor of n, for any n>1.
%C GCD(n, a(n))>1, for any n>1.
%H Paul Tek, <a href="/A256508/b256508.txt">Table of n, a(n) for n = 1..10000</a>
%H Paul Tek, <a href="/A256508/a256508.pl.txt">Perl program for this sequence</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Iterated_function#Definition">Iterated function</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e a^1(1)=a(1)=1.
%e a^2(2)=a(a(2))=a(4)=2.
%e a^3(3)=a(a(a(3)))=a(a(6))=a(9)=3.
%o (Perl) See Links section.
%Y Cf. A256513.
%K nonn,nice
%O 1,2
%A _Paul Tek_, Mar 31 2015
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