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A329896 Lexicographically earliest infinite sequence such that a(i) = a(j) => A219175(i) = A219175(j) and A322592(i) = A322592(j) for all i, j.

%I A329896 #6 Dec 07 2019 17:23:36
%S A329896 1,1,2,3,2,3,2,4,5,6,2,4,2,7,8,9,2,10,2,9,11,12,2,13,14,15,16,17,2,18,
%T A329896 2,19,20,21,22,23,2,24,25,26,2,23,2,27,28,29,2,26,30,31,32,33,2,34,35,
%U A329896 36,37,38,2,26,2,39,40,41,42,43,2,44,45,46,2,47,2,48,35,49,50,51,2,52,53,54,2,47,55,56,57,58,2,51,59,60,61,62,63,64,2,65,66,67,2,68,2,69,70
%N A329896 Lexicographically earliest infinite sequence such that a(i) = a(j) => A219175(i) = A219175(j) and A322592(i) = A322592(j) for all i, j.
%H A329896 Antti Karttunen, <a href="/A329896/b329896.txt">Table of n, a(n) for n = 1..65537</a>
%o A329896 (PARI)
%o A329896 up_to = 65537;
%o A329896 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 A329896 A219175(n) = (n%lcm(znstar(n)[2]));
%o A329896 A289625(n) = { my(m=1,p=2,v=znstar(n)[2]); for(i=1,length(v),m *= p^v[i]; p = nextprime(p+1)); (m); };
%o A329896 Aux329896(n) = if((n>2)&&isprime(n),0,[A219175(n),A289625(n)]);
%o A329896 v329896 = rgs_transform(vector(up_to, n, Aux329896(n)));
%o A329896 A329896(n) = v329896[n];
%Y A329896 Cf. A002322, A219175, A289625, A322592, A327979, A329895.
%K A329896 nonn
%O A329896 1,3
%A A329896 _Antti Karttunen_, Dec 07 2019