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A322592 Lexicographically earliest such sequence a that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 for odd primes, and f(n) = A289625(n) for any other number.

%I A322592 #6 Dec 18 2018 17:05:00
%S A322592 1,1,2,3,2,3,2,4,5,6,2,4,2,5,7,7,2,5,2,7,8,9,2,10,11,12,13,8,2,7,2,14,
%T A322592 15,16,17,8,2,13,17,18,2,8,2,15,17,19,2,18,20,11,21,17,2,13,22,23,24,
%U A322592 25,2,18,2,26,27,21,28,15,2,21,29,17,2,23,2,30,22,24,31,17,2,32,33,34,2,23,35,20,36,37,2,17,38,29,31,39,40,41,2,20,31,22,2,21,2,42,42
%N A322592 Lexicographically earliest such sequence a that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 for odd primes, and f(n) = A289625(n) for any other number.
%C A322592 For all i, j:
%C A322592   a(i) = a(j) => A034380(i) = A034380(j),
%C A322592   a(i) = a(j) => A104194(i) = A104194(j),
%C A322592   a(i) = a(j) => A290084(i) = A290084(j).
%H A322592 Antti Karttunen, <a href="/A322592/b322592.txt">Table of n, a(n) for n = 1..65537</a>
%o A322592 (PARI)
%o A322592 default(parisizemax,2^31);
%o A322592 up_to = 65537;
%o A322592 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 A322592 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 A322592 Aux322592(n) = if((n>2)&&isprime(n),0,A289625(n));
%o A322592 v322592 = rgs_transform(vector(up_to, n, Aux322592(n)));
%o A322592 A322592(n) = v322592[n];
%o A322592 for(n=1,up_to,write("b322592.txt", n, " ", A322592(n)));
%Y A322592 Cf. A289625, A289626, A322587, A322588, A322589, A322591.
%K A322592 nonn
%O A322592 1,3
%A A322592 _Antti Karttunen_, Dec 18 2018