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A329048 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329038(i) = A329038(j) for all i, j.

%I A329048 #10 Nov 11 2019 18:43:13
%S A329048 1,2,2,3,4,5,2,6,3,7,8,9,4,10,5,11,12,13,14,15,16,17,18,19,20,21,22,
%T A329048 23,24,25,2,26,6,27,28,29,3,30,7,31,32,33,8,34,9,35,36,37,38,39,40,41,
%U A329048 42,43,44,45,46,47,48,49,4,50,10,51,52,53,5,54,11,55,56,57,12,58,13,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,14,74,15,75,76,77,16
%N A329048 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329038(i) = A329038(j) for all i, j.
%C A329048 Restricted growth sequence transform of A329038, i.e., of function f(n) = A246277(A276086(n)).
%C A329048 For all i, j:
%C A329048   a(i) = a(j) => A286626(i) = A286626(j),
%C A329048   a(i) = a(j) => A276088(i) = A276088(j),
%C A329048   a(i) = a(j) => A276153(i) = A276153(j),
%H A329048 Antti Karttunen, <a href="/A329048/b329048.txt">Table of n, a(n) for n = 0..32768</a>
%o A329048 (PARI)
%o A329048 up_to = 32768;
%o A329048 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 A329048 A246277(n) = if(1==n, 0, my(f = factor(n), k = primepi(f[1,1])-1); for (i=1, #f~, f[i,1] = prime(primepi(f[i,1])-k)); factorback(f)/2);
%o A329048 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A329048 A329038(n) = A246277(A276086(n));
%o A329048 v329048 = rgs_transform(vector(1+up_to, n, A329038(n-1)));
%o A329048 A329048(n) = v329048[1+n];
%Y A329048 Cf. A046523, A246277, A276086, A276088, A276153, A278226, A286626, A329038.
%Y A329048 Cf. also A329345.
%K A329048 nonn
%O A329048 0,2
%A A329048 _Antti Karttunen_, Nov 11 2019