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A339811 Lexicographically earliest infinite sequence such that a(i) = a(j) => A339810(i) = A339810(j), for all i, j >= 1.

%I A339811 #5 Dec 19 2020 07:59:21
%S A339811 1,2,2,3,3,4,2,4,2,5,2,4,4,6,4,4,4,7,4,6,2,5,4,5,5,8,2,9,2,4,2,5,3,4,
%T A339811 4,10,4,4,2,11,2,12,4,4,5,11,2,4,8,5,2,13,2,14,2,15,8,8,4,16,2,4,2,17,
%U A339811 4,5,2,11,3,4,2,4,4,5,4,18,4,6,4,8,2,19,4,4,8,5,4,11,2,8,2,12,4,4,4,11,20,4,5,19,3,4,4,4,4
%N A339811 Lexicographically earliest infinite sequence such that a(i) = a(j) => A339810(i) = A339810(j), for all i, j >= 1.
%H A339811 Antti Karttunen, <a href="/A339811/b339811.txt">Table of n, a(n) for n = 1..65537</a>
%o A339811 (PARI)
%o A339811 up_to = 65537;
%o A339811 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 A339811 A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
%o A339811 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A339811 A339810(n) = A046523(A019565(n)-1);
%o A339811 v339811 = rgs_transform(vector(up_to, n, A339810(n)));
%o A339811 A339811(n) = v339811[n];
%Y A339811 Cf. A019565, A046523, A339809, A339810, A339812.
%K A339811 nonn
%O A339811 1,2
%A A339811 _Antti Karttunen_, Dec 18 2020