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A328577 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(0) = 0 and f(n>0) = A328572(n), for all i, j.

%I A328577 #5 Oct 20 2019 21:45:46
%S A328577 1,2,2,2,3,3,2,2,2,2,3,3,4,4,4,4,5,5,6,6,6,6,7,7,8,8,8,8,9,9,2,2,2,2,
%T A328577 3,3,2,2,2,2,3,3,4,4,4,4,5,5,6,6,6,6,7,7,8,8,8,8,9,9,10,10,10,10,11,
%U A328577 11,10,10,10,10,11,11,12,12,12,12,13,13,14,14,14,14,15,15,16,16,16,16,17,17,18,18,18,18,19,19,18,18,18,18,19,19,20,20,20,20
%N A328577 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(0) = 0 and f(n>0) = A328572(n), for all i, j.
%C A328577 Restricted growth sequence transform of function f, defined as: f(0) = 0 and for n > 0, f(n) = A328572(n) = A003557(A276086(n)).
%C A328577 For all i, j: a(i) = a(j) => A328114(i) = A328114(j).
%H A328577 Antti Karttunen, <a href="/A328577/b328577.txt">Table of n, a(n) for n = 0..32768</a>
%H A328577 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A328577 (PARI)
%o A328577 up_to = 32768;
%o A328577 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 A328577 A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };
%o A328577 Aux328577(n) = if(!n,n,A328572(n));
%o A328577 v328577 = rgs_transform(vector(1+up_to, n, Aux328577(n-1)));
%o A328577 A328577(n) = v328577[1+n];
%Y A328577 Cf. A003557, A276086, A328114, A328572, A328576.
%K A328577 nonn
%O A328577 0,2
%A A328577 _Antti Karttunen_, Oct 20 2019