%I #10 Dec 27 2018 17:36:04
%S 1,2,3,4,3,5,3,4,6,7,3,5,3,8,7,4,3,5,3,7,9,10,3,5,11,12,6,8,3,13,3,4,
%T 14,15,8,5,3,16,17,7,3,18,3,10,7,19,3,5,20,7,21,12,3,5,14,8,22,23,3,
%U 13,3,24,9,4,25,26,3,15,27,18,3,5,3,28,7,16,10,29,3,7,6,30,3,18,31,32,33,10,3,13,17,19,34,35,36,5,3,8,14,7,3,37,3,12,18
%N Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(2) = -1, f(n) = 0 if n is an odd prime, and f(n) = A278221(n) for all other numbers.
%C For all i, j: a(i) = a(j) => A001221(i) = A001221(j).
%H Antti Karttunen, <a href="/A322814/b322814.txt">Table of n, a(n) for n = 1..65537</a>
%o (PARI)
%o up_to = 4096;
%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 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%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 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
%o A322814aux(n) = if(2==n,-1,if(isprime(n),0,A046523(A122111(n))));
%o v322814 = rgs_transform(vector(up_to,n,A322814aux(n)));
%o A322814(n) = v322814[n];
%Y Cf. A046523, A122111, A278221, A286621, A318890.
%K nonn
%O 1,2
%A _Antti Karttunen_, Dec 27 2018