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A329381 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329380(i) = A329380(j) for all i, j.

%I A329381 #6 Nov 12 2019 19:21:16
%S A329381 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,18,19,20,2,
%T A329381 21,2,22,23,24,25,26,2,27,28,29,2,30,2,16,31,32,2,33,34,35,36,37,2,38,
%U A329381 39,40,41,42,2,43,2,44,45,46,47,48,2,49,50,51,2,52,2,53,54,55,47,56,2,57,58,59,2,60,61,62,63,64,2,65,66,67,68,69,70,71,2,72,73
%N A329381 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329380(i) = A329380(j) for all i, j.
%C A329381 Restricted growth sequence transform of A329380.
%C A329381 For all i, j:
%C A329381   A305800(i) = A305800(j) => a(i) = a(j),
%C A329381   a(i) = a(j) => A323599(i) = A323599(j).
%H A329381 Antti Karttunen, <a href="/A329381/b329381.txt">Table of n, a(n) for n = 1..65537</a>
%o A329381 (PARI)
%o A329381 up_to = 65537;
%o A329381 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 A329381 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A329381 A329380(n) = { my(m=1); fordiv(n,d,m *= A276086(d)^omega(n/d)); (m); };
%o A329381 v329381 = rgs_transform(vector(up_to, n, A329380(n)));
%o A329381 A329381(n) = v329381[n];
%Y A329381 Cf. A001221, A276086, A305800, A323599, A329380.
%Y A329381 Cf. also A329351.
%K A329381 nonn
%O A329381 1,2
%A A329381 _Antti Karttunen_, Nov 12 2019