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A328388 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A327860(i)) = A046523(A327860(j)) for all i, j >= 0.

%I A328388 #12 Feb 01 2022 18:12:58
%S A328388 1,2,2,3,4,4,2,3,5,3,4,4,4,6,4,4,7,8,6,6,9,6,9,9,10,11,11,10,12,13,2,
%T A328388 14,4,3,4,8,6,3,3,4,8,4,4,4,9,6,8,8,9,9,6,6,15,9,13,11,13,11,16,13,4,
%U A328388 4,4,4,17,8,4,8,8,4,9,8,12,8,8,18,19,18,9,9,20,21,17,17,12,12,13,12,22,23,6,6,24,6,9,9,9,6,6,6,25,17,9,17,17,9
%N A328388 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A327860(i)) = A046523(A327860(j)) for all i, j >= 0.
%C A328388 Restricted growth sequence transform of A046523(A327860(n)).
%H A328388 Antti Karttunen, <a href="/A328388/b328388.txt">Table of n, a(n) for n = 0..30030</a>
%o A328388 (PARI)
%o A328388 up_to = 30030;
%o A328388 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 A328388 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A328388 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A328388 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328388 A327860(n) = A003415(A276086(n));
%o A328388 Aux328388(n) = if(!n,0,A046523(A327860(n)));
%o A328388 v328388 = rgs_transform(vector(1+up_to, n, Aux328388(n-1)));
%o A328388 A328388(n) = v328388[1+n];
%Y A328388 Cf. A003415, A046523, A276086, A327860.
%Y A328388 Cf. also A286626 (compare the scatter plots).
%K A328388 nonn,easy,look
%O A328388 0,2
%A A328388 _Antti Karttunen_, Oct 15 2019