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A262599 Lexicographically earliest sequence of distinct terms such that, for any n > 0, phi(a(n)) = phi(n) (where phi denotes the Euler totient function), and a(n) > n if possible.

%I A262599 #18 Sep 30 2024 14:18:40
%S A262599 2,1,4,6,8,3,9,10,14,12,22,5,21,18,16,20,32,7,27,24,26,11,46,30,33,28,
%T A262599 38,36,58,15,62,34,44,40,39,42,57,54,45,48,55,13,49,50,52,23,94,60,86,
%U A262599 66,64,56,106,19,75,70,63,29,118,17,77,31,74,68,104,25
%N A262599 Lexicographically earliest sequence of distinct terms such that, for any n > 0, phi(a(n)) = phi(n) (where phi denotes the Euler totient function), and a(n) > n if possible.
%C A262599 This is a permutation of the positive integers, with inverse A262603.
%C A262599 If the Carmichael's totient function conjecture is true, then this sequence has no fixed point.
%C A262599 For any n > 0, the orbit of n is finite, with length A066412(n).
%H A262599 Paul Tek, <a href="/A262599/b262599.txt">Table of n, a(n) for n = 1..10000</a>
%H A262599 Paul Tek, <a href="/A262599/a262599.cpp.txt">C program for this sequence</a>
%H A262599 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A262599 a(n) = max(A066659(n), A049283(A000010(n))), for any n > 0.
%e A262599 phi(n) = 6 iff n is in { 7, 9, 14, 18 }.
%e A262599 Hence: a(7) = 9, a(9) = 14, a(14) = 18, a(18) = 7.
%o A262599 (C) // See Links section for C program.
%Y A262599 Cf. A049283, A066412, A066659, A262603 (inverse).
%K A262599 nonn
%O A262599 1,1
%A A262599 _Paul Tek_, Sep 25 2015