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A328395 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A276087(i)) = A046523(A276087(j)) for all i, j.

%I A328395 #10 Oct 16 2019 13:19:06
%S A328395 1,1,2,1,3,4,5,5,6,1,7,4,8,9,10,11,7,5,12,7,13,14,15,16,17,18,19,20,
%T A328395 21,22,2,5,9,5,6,8,6,23,24,1,25,4,26,27,28,11,29,8,30,31,32,33,34,35,
%U A328395 36,37,38,39,40,41,9,9,42,12,24,12,7,43,44,45,46,47,48,27,49,33,50,35,51,52,53,54,55,56,57,58,59,20,60,61,30,27,62,63,64,65,66,15,67,68,69,8
%N A328395 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A276087(i)) = A046523(A276087(j)) for all i, j.
%C A328395 Restricted growth sequence transform of function f(n) = A278226(A276086(n)) = A046523(A276086(A276086(n))).
%C A328395 For all i, j:
%C A328395   a(i) = a(j) => A328397(i) = A328397(j) => A328389(i) = A328389(j).
%H A328395 Antti Karttunen, <a href="/A328395/b328395.txt">Table of n, a(n) for n = 0..32589</a>
%H A328395 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A328395 (PARI)
%o A328395 up_to = 32589;
%o A328395 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 A328395 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A328395 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328395 A276087(n) = A276086(A276086(n));
%o A328395 v328395 = rgs_transform(vector(1+up_to, n, A046523(A276087(n-1))));
%o A328395 A328395(n) = v328395[1+n];
%Y A328395 Cf. A046523, A276086, A276087, A328389.
%Y A328395 Cf. A143293 (positions of 1's after the initial one).
%Y A328395 Cf. also A278226, A286626, A328388, A328396, A328397.
%K A328395 nonn
%O A328395 0,3
%A A328395 _Antti Karttunen_, Oct 15 2019