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A329351 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329350(i) = A329350(j) for all i, j.

%I A329351 #7 Nov 12 2019 19:20:15
%S A329351 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,4,12,9,17,2,
%T A329351 18,2,19,20,21,22,23,2,24,25,26,2,27,2,28,29,30,2,31,32,33,34,35,2,36,
%U A329351 37,38,39,18,2,40,2,41,42,43,44,45,2,46,47,48,2,49,2,50,51,52,44,53,2,54,55,56,2,57,58,59,60,61,2,62,63,64,65,66,29,67,2,68,69
%N A329351 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329350(i) = A329350(j) for all i, j.
%C A329351 Restricted growth sequence transform of A329350.
%C A329351 For all i, j:
%C A329351   A305800(i) = A305800(j) => a(i) = a(j),
%C A329351   a(i) = a(j) => A069359(i) = A069359(j).
%H A329351 Antti Karttunen, <a href="/A329351/b329351.txt">Table of n, a(n) for n = 1..65537</a>
%o A329351 (PARI)
%o A329351 up_to = 65537;
%o A329351 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 A329351 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A329351 A329350(n) = { my(m=1); fordiv(n,d,if(isprime(n/d), m *= A276086(d))); (m); };
%o A329351 v329351 = rgs_transform(vector(up_to, n, A329350(n)));
%o A329351 A329351(n) = v329351[n];
%Y A329351 Cf. A069359, A305800, A329350.
%Y A329351 Cf. also A329353, A329381.
%K A329351 nonn
%O A329351 1,2
%A A329351 _Antti Karttunen_, Nov 12 2019