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A336648 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336476(i) = A336476(j), for all i, j >= 1.

%I A336648 #5 Jul 31 2020 16:42:37
%S A336648 1,1,2,1,2,2,2,1,1,2,2,2,2,2,3,1,2,1,2,2,4,2,2,2,1,2,4,2,2,3,2,1,3,2,
%T A336648 4,1,2,2,4,2,2,4,2,2,5,2,2,2,6,1,3,2,2,4,4,2,4,2,2,3,2,2,2,1,4,3,2,2,
%U A336648 3,4,2,1,2,2,2,2,4,4,2,2,1,2,2,4,4,2,3,2,2,5,7,2,4,2,8,2,2,6,5,1,2,3,2,2,9
%N A336648 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336476(i) = A336476(j), for all i, j >= 1.
%C A336648 Restricted growth sequence transform of A336476.
%C A336648 For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).
%H A336648 Antti Karttunen, <a href="/A336648/b336648.txt">Table of n, a(n) for n = 1..65537</a>
%o A336648 (PARI)
%o A336648 up_to = 65537;
%o A336648 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 A336648 A000593(n) = sigma(n>>valuation(n, 2));
%o A336648 A336475(n) = { my(f=factor(n)); prod(i=1, #f~, if(2==f[i,1],1,(1+f[i,2]) * (f[i,1]^f[i,2]))); };
%o A336648 A336476(n) = gcd(A000593(n), A336475(n));
%o A336648 v336648 = rgs_transform(vector(up_to,n,A336476(n)));
%o A336648 A336648(n) = v336648[n];
%Y A336648 Cf. A000593, A336475, A336476.
%Y A336648 Cf. also A003602, A324400, A336320.
%K A336648 nonn
%O A336648 1,3
%A A336648 _Antti Karttunen_, Jul 31 2020