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%I #10 Jan 04 2019 09:05:16
%S 1,2,3,3,4,4,5,6,6,5,7,8,9,7,8,10,11,12,13,14,14,9,15,16,12,11,10,17,
%T 18,19,20,21,17,13,19,22,23,15,24,25,26,27,28,24,16,18,29,30,31,31,32,
%U 32,33,34,27,35,36,20,37,38,39,23,25,40,41,41,42,36,43,44,45,46,47,26,22,43,44,48,49,50,21,28,51,52,48,29,53,54,55,56,57,53,58,33,59,60,61,62,35,63,64,59,65,66,38
%N Lexicographically earliest such sequence a that for all i, j, a(i) = a(j) => f(i) = f(j), where f(1)=0, and f(n) = A252463(n) for n > 1.
%C For all i, j:
%C a(i) = a(j) => A252463(i) = A252463(j) => A285727(i) = A285727(j),
%C a(i) = a(j) => A320110(i) = A320110(j) => A320111(i) = A320111(j).
%H Antti Karttunen, <a href="/A323080/b323080.txt">Table of n, a(n) for n = 1..65537</a>
%o (PARI)
%o up_to = 65537;
%o 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 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A252463(n) = if(!(n%2),n/2,A064989(n));
%o A323080aux(n) = if(1==n,0,A252463(n));
%o v323080 = rgs_transform(vector(up_to,n,A323080aux(n)));
%o A323080(n) = v323080[n];
%Y Cf. A252463, A285727, A320107, A320110, A320111, A322805, A323081.
%K nonn,look
%O 1,2
%A _Antti Karttunen_, Jan 03 2019
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