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A329606 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329605(i) = A329605(j) for all i, j.

%I A329606 #6 Nov 18 2019 16:42:11
%S A329606 1,2,3,4,5,6,7,3,8,9,10,5,11,12,13,14,15,9,16,7,17,18,19,20,21,22,7,
%T A329606 10,23,12,24,6,25,26,27,28,29,30,31,32,33,18,34,11,10,35,36,9,37,17,
%U A329606 38,15,39,32,40,41,42,43,44,45,46,47,11,48,49,22,50,16,51,25,52,13,53,54,18,19,55,26,56,12,57,58,59,60,61,62,63,64,65,41,66,23,67,68,69,70,71,40,15,72,73,30,74,75,22
%N A329606 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329605(i) = A329605(j) for all i, j.
%C A329606 Restricted growth sequence transform of A329605(n) = A000005(A108951(n)).
%C A329606 For all i, j:
%C A329606   a(i) = a(j) => A329614(i) = A329614(j).
%H A329606 Antti Karttunen, <a href="/A329606/b329606.txt">Table of n, a(n) for n = 1..100000</a>
%H A329606 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A329606 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%o A329606 (PARI)
%o A329606 up_to = 100000;
%o A329606 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 A329606 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A329606 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
%o A329606 A329605(n) = numdiv(A108951(n));
%o A329606 v329606 = rgs_transform(vector(up_to, n, A329605(n)));
%o A329606 A329606(n) = v329606[n];
%Y A329606 Cf. A000005, A108951, A329605, A329608, A329614.
%K A329606 nonn
%O A329606 1,2
%A A329606 _Antti Karttunen_, Nov 18 2019