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A326203 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n > 2 and gcd(n,phi(n)) = 1, with f(n) = n for all other numbers.

%I A326203 #7 Jul 11 2019 15:48:11
%S A326203 1,2,3,4,3,5,3,6,7,8,3,9,3,10,3,11,3,12,3,13,14,15,3,16,17,18,19,20,3,
%T A326203 21,3,22,3,23,3,24,3,25,26,27,3,28,3,29,30,31,3,32,33,34,3,35,3,36,37,
%U A326203 38,39,40,3,41,3,42,43,44,3,45,3,46,3,47,3,48,3,49,50,51,3,52,3,53,54,55,3,56,3,57,3,58,3,59,3,60,61,62,3,63,3,64,65,66,3,67,3
%N A326203 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n > 2 and gcd(n,phi(n)) = 1, with f(n) = n for all other numbers.
%C A326203 For all i, j:
%C A326203   A305801(i) = A305801(j) => a(i) = a(j),
%C A326203   a(i) = a(j) => A009195(i) = A009195(j) => A297086(i) = A297086(j),
%C A326203   a(i) = a(j) => A000001(i) = A000001(j) => A297086(i) = A297086(j).
%H A326203 Antti Karttunen, <a href="/A326203/b326203.txt">Table of n, a(n) for n = 1..65537</a>
%o A326203 (PARI)
%o A326203 up_to = 65537;
%o A326203 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A326203 Aux326203(n) = if((n>2) && (1==gcd(n,eulerphi(n))),0,n);
%o A326203 v326203 = rgs_transform(vector(up_to, n, Aux326203(n)));
%o A326203 A326203(n) = v326203[n];
%Y A326203 Cf. A000001, A000010, A003277, A009195, A297086, A305801.
%Y A326203 Cf. also A326201, A326202.
%K A326203 nonn
%O A326203 1,2
%A A326203 _Antti Karttunen_, Jul 11 2019