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A322826 Lexicographically earliest such sequence a that a(i) = a(j) => A052126(i) = A052126(j) for all i, j.

%I A322826 #14 Dec 28 2018 10:03:00
%S A322826 1,1,1,2,1,2,1,3,4,2,1,3,1,2,4,5,1,6,1,3,4,2,1,5,7,2,8,3,1,6,1,9,4,2,
%T A322826 7,10,1,2,4,5,1,6,1,3,8,2,1,9,11,12,4,3,1,13,7,5,4,2,1,10,1,2,8,14,7,
%U A322826 6,1,3,4,12,1,15,1,2,16,3,11,6,1,9,17,2,1,10,7,2,4,5,1,13,11,3,4,2,7,14,1,18,8,19,1,6,1,5,16
%N A322826 Lexicographically earliest such sequence a that a(i) = a(j) => A052126(i) = A052126(j) for all i, j.
%C A322826 Restricted growth sequence transform of A052126, or equally, of A322820.
%C A322826 For all i, j:
%C A322826   A300226(i) = A300226(j) => a(i) = a(j),
%C A322826   a(i) = a(j) => A322813(i) = A322813(j),
%C A322826   a(i) = a(j) => A322819(i) = A322819(j).
%C A322826 For all i, j > 1:
%C A322826   a(i) = a(j) => A001222(i) = A001222(j).
%H A322826 Antti Karttunen, <a href="/A322826/b322826.txt">Table of n, a(n) for n = 1..65537</a>
%o A322826 (PARI)
%o A322826 up_to = 65537;
%o A322826 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 A322826 A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
%o A322826 A052126(n) = (n/A006530(n));
%o A322826 v322826 = rgs_transform(vector(up_to,n,A052126(n)));
%o A322826 A322826(n) = v322826[n];
%Y A322826 Cf. A001222, A006530, A052126, A305800, A300226, A319994, A319996, A322813, A322819, A322820.
%K A322826 nonn
%O A322826 1,4
%A A322826 _Antti Karttunen_, Dec 27 2018