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A350064 Lexicographically earliest infinite sequence such that a(i) = a(j) => A350062(i) = A350062(j), for all i, j >= 1.

%I A350064 #11 Jan 29 2022 22:32:20
%S A350064 1,2,3,3,4,3,5,3,6,4,7,3,8,3,6,6,9,3,10,3,11,6,12,3,11,6,6,6,13,6,14,
%T A350064 3,6,6,11,5,15,3,16,6,17,3,18,3,6,19,20,3,19,4,16,3,21,3,22,3,16,11,
%U A350064 23,3,24,6,6,11,11,6,25,6,6,3,26,6,27,6,6,6,19,6,28,3,16,6,29,11,30,16,31,19,32,11,33,6,30,30,30
%N A350064 Lexicographically earliest infinite sequence such that a(i) = a(j) => A350062(i) = A350062(j), for all i, j >= 1.
%C A350064 Restricted growth sequence transform of A350062.
%C A350064 For all i, j >= 1: a(i) = a(j) => A324105(i) = A324105(j).
%C A350064 For all i, j >= 2:
%C A350064   a(i) = a(j) => A324119(i) = A324119(j),
%C A350064   a(i) = a(j) => A342655(i) = A342655(j).
%H A350064 Antti Karttunen, <a href="/A350064/b350064.txt">Table of n, a(n) for n = 1..10000</a> (based on Hans Havermann's factorization of A156552)
%H A350064 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o A350064 (PARI)
%o A350064 up_to = 3000;
%o A350064 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 A350064 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A350064 A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A350064 A350062(n) = if(1==n,0,A046523(A156552(n)));
%o A350064 v350064 = rgs_transform(vector(up_to, n, A350062(n)));
%o A350064 A350064(n) = v350064[n];
%Y A350064 Cf. A046523, A156552, A350062, A350065.
%Y A350064 Cf. also A286621, A324105, A324119, A342655.
%K A350064 nonn
%O A350064 1,2
%A A350064 _Antti Karttunen_, Jan 29 2022