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A328397 Lexicographically earliest infinite sequence such that a(i) = a(j) => A328400(A276087(i)) = A328400(A276087(j)) for all i, j.

%I A328397 #6 Oct 16 2019 13:19:25
%S A328397 1,1,1,1,1,2,3,3,3,1,3,2,4,5,3,6,3,3,7,3,8,9,8,10,11,12,13,14,15,16,1,
%T A328397 3,5,3,3,4,3,3,17,1,17,2,18,19,17,6,20,4,7,21,17,22,23,24,25,26,27,28,
%U A328397 23,21,5,5,4,7,17,7,3,3,17,29,30,31,18,19,32,22,33,24,34,35,36,37,38,39,15,40,41,14,42,43,7,19,44,45,19,46,21,8,17,47,48,4,49
%N A328397 Lexicographically earliest infinite sequence such that a(i) = a(j) => A328400(A276087(i)) = A328400(A276087(j)) for all i, j.
%C A328397 Restricted growth sequence transform of function f(n) = A328400(A276087(n)).
%C A328397 For all i, j:
%C A328397    A328395(i) = A328395(j) => a(i) = a(j) => A328389(i) = A328389(j).
%H A328397 Antti Karttunen, <a href="/A328397/b328397.txt">Table of n, a(n) for n = 0..32589</a>
%H A328397 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A328397 (PARI)
%o A328397 up_to = 32589;
%o A328397 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 A328397 A007947(n) = factorback(factorint(n)[, 1]);
%o A328397 A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
%o A328397 A181821(n) = { my(f=factor(n),p=0,m=1); forstep(i=#f~,1,-1,while(f[i,2], f[i,2]--; m *= (p=nextprime(p+1))^primepi(f[i,1]))); (m); };
%o A328397 A328400(n) = A181821(A007947(A181819(n)));
%o A328397 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328397 A276087(n) = A276086(A276086(n));
%o A328397 v328397 = rgs_transform(vector(1+up_to, n, A328400(A276087(n-1))));
%o A328397 A328397(n) = v328397[1+n];
%Y A328397 Cf. A276086, A276087, A328389, A328400.
%Y A328397 Cf. also A278226, A286626, A328388, A328395, A328396.
%K A328397 nonn
%O A328397 0,6
%A A328397 _Antti Karttunen_, Oct 15 2019