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A334869 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 1, where f(1) = 0 and for n > 1, f(n) = A334870(n).

%I A334869 #7 Jun 09 2020 22:11:27
%S A334869 1,2,3,3,4,5,6,7,5,8,9,10,11,12,13,7,14,15,16,17,18,19,20,21,8,22,23,
%T A334869 24,25,26,27,28,29,30,31,4,32,33,34,35,36,37,38,39,40,41,42,43,12,44,
%U A334869 45,46,47,48,49,50,51,52,53,54,55,56,57,10,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,15,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,13,92
%N A334869 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 1, where f(1) = 0 and for n > 1, f(n) = A334870(n).
%H A334869 Antti Karttunen, <a href="/A334869/b334869.txt">Table of n, a(n) for n = 1..65537</a>
%o A334869 (PARI)
%o A334869 up_to = 65537;
%o A334869 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 A334869 A334870(n) = if(issquare(n),sqrtint(n),my(c=core(n), m=n); forprime(p=2, , if(!(c % p), m/=p; break, m*=p)); (m));
%o A334869 A334869aux(n) = if(1==n,0,A334870(n));
%o A334869 v334869 = rgs_transform(vector(up_to,n,A334869aux(n)));
%o A334869 A334869(n) = v334869[n];
%Y A334869 Cf. A334868, A334870, A334871.
%K A334869 nonn
%O A334869 1,2
%A A334869 _Antti Karttunen_, Jun 08 2020