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A328576 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(0) = 0 and for n > 0, f(n) = [A276088(n), A328575(n)], for all i, j.

%I A328576 #6 Oct 20 2019 21:45:54
%S A328576 1,2,2,2,3,4,2,2,2,2,3,4,3,5,5,5,6,7,8,9,9,9,10,11,12,13,13,13,14,15,
%T A328576 2,2,2,2,3,4,2,2,2,2,3,4,3,5,5,5,6,7,8,9,9,9,10,11,12,13,13,13,14,15,
%U A328576 3,16,16,16,17,18,16,16,16,16,17,18,17,19,19,19,20,21,22,23,23,23,24,25,26,27,27,27,28,29,30,31,31,31,32,33,31,31,31,31,32,33
%N A328576 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(0) = 0 and for n > 0, f(n) = [A276088(n), A328575(n)], for all i, j.
%C A328576 Restricted growth sequence transform of function f, defined as: f(0) = 0 and for n > 0, f(n) = [A276088(n), A328575(n)].
%C A328576 For all i, j: a(i) = a(j) => A328114(i) = A328114(j).
%H A328576 Antti Karttunen, <a href="/A328576/b328576.txt">Table of n, a(n) for n = 0..32768</a>
%H A328576 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A328576 (PARI)
%o A328576 up_to = 32768;
%o A328576 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 A328576 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
%o A328576 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
%o A328576 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328576 A276088(n) = { my(e=0, p=2); while(n && !(e=(n%p)), n = n/p; p = nextprime(1+p)); (e); };
%o A328576 A328575(n) = A003557(A032742(A276086(n)));
%o A328576 Aux328576(n) = if(!n,n,[A276088(n), A328575(n)]);
%o A328576 v328576 = rgs_transform(vector(1+up_to, n, Aux328576(n-1)));
%o A328576 A328576(n) = v328576[1+n];
%Y A328576 Cf. A003557, A032742, A276086, A276088, A328114, A328575, A328577.
%K A328576 nonn
%O A328576 0,2
%A A328576 _Antti Karttunen_, Oct 20 2019