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A329345 Lexicographically earliest infinite sequence such that a(i) = a(j) => A246277(A329044(i)) = A246277(A329044(j)) for all i, j.

%I A329345 #8 Nov 11 2019 18:43:45
%S A329345 1,2,2,3,2,3,2,4,4,3,2,5,2,3,6,7,2,7,2,5,6,3,2,8,9,3,10,5,2,11,2,10,6,
%T A329345 3,12,13,2,3,6,4,2,4,2,5,14,3,2,15,16,17,6,5,2,18,19,20,6,3,2,21,2,3,
%U A329345 21,18,22,23,2,5,6,24,2,25,2,3,26,5,27,23,2,7,28,3,2,7,29,3,6,20,2,30,31,5,6,3,32,33,2,34,35,16,2,23,2,20,36
%N A329345 Lexicographically earliest infinite sequence such that a(i) = a(j) => A246277(A329044(i)) = A246277(A329044(j)) for all i, j.
%C A329345 Restricted growth sequence transform of function f(n) = A246277(A329044(n)).
%C A329345 For all i, j:
%C A329345   A305800(i) = A305800(j) => a(i) = a(j),
%C A329345   a(i) = a(j) => A329045(i) = A329045(j),
%C A329345   a(i) = a(j) => A329343(i) = A329343(j),
%C A329345   a(i) = a(j) => A329348(i) = A329348(j),
%C A329345   a(i) = a(j) => A329349(i) = A329349(j).
%H A329345 Antti Karttunen, <a href="/A329345/b329345.txt">Table of n, a(n) for n = 1..65537</a>
%H A329345 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A329345 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A329345 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%o A329345 (PARI)
%o A329345 up_to = 1024;
%o A329345 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 A329345 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A329345 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
%o A329345 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A329345 A324886(n) = A276086(A108951(n));
%o A329345 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A329345 A329044(n) = A064989(A324886(n));
%o A329345 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 A329345 v329345 = rgs_transform(vector(up_to, n, A246277(A329044(n))));
%o A329345 A329345(n) = v329345[n];
%Y A329345 Cf. A034386, A064989, A108951, A246277, A276086, A305800, A324886, A329044, A329045, A329343, A329348, A329349.
%Y A329345 Cf. also A329048.
%K A329345 nonn
%O A329345 1,2
%A A329345 _Antti Karttunen_, Nov 11 2019