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A300223 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A296091(i) = A296091(j), for all i, j >= 1.

%I A300223 #12 May 20 2022 23:04:30
%S A300223 1,2,2,3,2,4,2,5,6,4,2,7,2,4,4,8,2,9,2,10,4,11,2,12,13,4,5,9,2,14,2,
%T A300223 15,4,4,4,16,2,4,11,12,2,17,2,10,9,4,2,18,19,20,4,10,2,21,4,21,4,4,2,
%U A300223 22,2,11,10,23,4,17,2,7,11,17,2,24,2,4,9,10,11,14,2,18,25,26,2,22,4,4,11,12,2,22,11,10,4,11,11,27,2,28,9,29,2,17,2,21,14
%N A300223 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A296091(i) = A296091(j), for all i, j >= 1.
%C A300223 Restricted growth sequence transform of the ordered pair [A046523(n), A296091(n)].
%H A300223 Antti Karttunen, <a href="/A300223/b300223.txt">Table of n, a(n) for n = 1..65537</a>
%o A300223 (PARI)
%o A300223 up_to = 65537;
%o A300223 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 A300223 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A300223 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A300223 A296091(n) = if(1==n,n,A046523(sigma(n)-1));
%o A300223 Aux300223(n) = (1/2)*(2 + ((A046523(n)+A296091(n))^2) - A046523(n) - 3*A296091(n));
%o A300223 v300223 = rgs_transform(vector(up_to,n,Aux300223(n)));
%o A300223 A300223(n) = v300223[n];
%Y A300223 Cf. A046523, A296091.
%Y A300223 Cf. also A305800, A296090, A300224, A300225.
%K A300223 nonn
%O A300223 1,2
%A A300223 _Antti Karttunen_, Mar 01 2018
%E A300223 Name changed by _Antti Karttunen_, May 20 2022