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A344594 Lexicographically earliest infinite sequence such that a(i) = a(j) => A342920(i) = A342920(j), for all i, j >= 1.

%I A344594 #11 May 28 2021 18:01:57
%S A344594 1,1,1,2,1,2,1,3,4,2,1,5,1,2,6,7,1,8,1,5,6,2,1,9,10,2,7,5,1,11,1,12,6,
%T A344594 2,13,14,1,2,6,15,1,8,1,5,16,2,1,17,18,19,6,5,1,20,21,3,6,2,1,22,1,2,
%U A344594 23,24,25,4,1,5,6,26,1,27,1,2,28,5,29,4,1,30,31,2,1,14,32,2,6,3,1,33,34,5,6,2,35,36,1,37,38,39,1,4,1,3,40
%N A344594 Lexicographically earliest infinite sequence such that a(i) = a(j) => A342920(i) = A342920(j), for all i, j >= 1.
%C A344594 Restricted growth sequence transform of A342920, where A342920(n) = A342002(A108951(n)) = A329047(n) / A344592(n).
%H A344594 Antti Karttunen, <a href="/A344594/b344594.txt">Table of n, a(n) for n = 1..65537</a>
%H A344594 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A344594 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%o A344594 (PARI)
%o A344594 up_to = 65537;
%o A344594 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 A344594 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A344594 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
%o A344594 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A344594 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A344594 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A344594 A342002(n) = { my(u=A276086(n)); (A003415(u) / A003557(u)); };
%o A344594 A342920(n) = A342002(A108951(n));
%o A344594 v344594 = rgs_transform(vector(up_to, n, A342920(n)));
%o A344594 A344594(n) = v344594[n];
%Y A344594 Cf. A108951, A324886, A329047, A342002, A342920, A344592.
%Y A344594 Cf. also A344593.
%K A344594 nonn
%O A344594 1,4
%A A344594 _Antti Karttunen_, May 26 2021