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A329620 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A046523(n), A246277(A324886(n))].

%I A329620 #6 Nov 18 2019 22:04:18
%S A329620 1,2,2,3,2,4,2,5,6,4,2,7,2,4,8,9,2,10,2,7,8,4,2,11,12,4,13,7,2,14,2,
%T A329620 15,8,4,16,17,2,4,8,18,2,19,2,7,20,4,2,21,22,23,8,7,2,24,25,26,8,4,2,
%U A329620 27,2,4,28,29,30,31,2,7,8,32,2,33,2,4,34,7,35,31,2,36,37,4,2,38,39,4,8,26,2,40,41,7,8,4,42,43,2,44,45,46,2,31,2,26,47
%N A329620 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A046523(n), A246277(A324886(n))].
%C A329620 Restricted growth sequence transform of the ordered pair [A046523(n), A246277(A324886(n))].
%C A329620 For all i, j:
%C A329620   A305800(i) = A305800(j) => a(i) = a(j),
%C A329620   a(i) = a(j) => A101296(i) = A101296(j),
%C A329620   a(i) = a(j) => A329345(i) = A329345(j),
%C A329620   a(i) = a(j) => A329618(i) = A329618(j),
%C A329620   a(i) = a(j) => A329619(i) = A329619(j).
%H A329620 Antti Karttunen, <a href="/A329620/b329620.txt">Table of n, a(n) for n = 1..100000</a>
%H A329620 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A329620 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A329620 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%o A329620 (PARI)
%o A329620 up_to = 8192;
%o A329620 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 A329620 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A329620 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A329620 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
%o A329620 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A329620 A324886(n) = A276086(A108951(n));
%o A329620 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 A329620 Aux329620(n) = [A046523(n), A246277(A324886(n))];
%o A329620 v329620 = rgs_transform(vector(up_to, n, Aux329620(n)));
%o A329620 A329620(n) = v329620[n];
%Y A329620 Cf. A046523, A034386, A108951, A246277, A276086, A305800, A324886, A329345, A329618, A329619.
%K A329620 nonn
%O A329620 1,2
%A A329620 _Antti Karttunen_, Nov 18 2019