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A328396 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = A046523(A276086(A003415(A276086(n)))).

%I A328396 #8 Oct 16 2019 13:19:16
%S A328396 1,2,2,3,2,4,2,5,5,5,6,7,3,8,7,9,5,10,11,11,12,13,14,15,16,17,18,19,
%T A328396 20,21,2,22,3,8,23,24,25,26,11,6,27,28,29,24,11,30,31,32,27,33,10,34,
%U A328396 35,36,37,38,39,19,40,41,3,42,43,44,25,45,46,11,9,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,4,69,70,71,72,73,74,32
%N A328396 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = A046523(A276086(A003415(A276086(n)))).
%C A328396 Restricted growth sequence transform of function f(n) = A278226(A327860(n)) = A046523(A276086(A003415(A276086(n)))).
%C A328396 For all i, j: a(i) = a(j) => A328392(i) = A328392(j).
%H A328396 Antti Karttunen, <a href="/A328396/b328396.txt">Table of n, a(n) for n = 0..30030</a>
%o A328396 (PARI)
%o A328396 up_to = 30030;
%o A328396 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 A328396 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A328396 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A328396 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328396 Aux328396(n) = A046523(A276086(A003415(A276086(n))));
%o A328396 v328396 = rgs_transform(vector(1+up_to, n, Aux328396(n-1)));
%o A328396 A328396(n) = v328396[1+n];
%Y A328396 Cf. A003415, A046523, A276086, A327860, A328392.
%Y A328396 Cf. also A278226, A286626, A328388, A328395.
%K A328396 nonn
%O A328396 0,2
%A A328396 _Antti Karttunen_, Oct 15 2019