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A339874 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A052126(n) for n > 1, and f(1) = 0.

%I A339874 #7 Dec 25 2020 19:31:16
%S A339874 1,2,2,3,2,3,2,4,5,3,2,4,2,3,5,6,2,7,2,4,5,3,2,6,8,3,9,4,2,7,2,10,5,3,
%T A339874 8,11,2,3,5,6,2,7,2,4,9,3,2,10,12,13,5,4,2,14,8,6,5,3,2,11,2,3,9,15,8,
%U A339874 7,2,4,5,13,2,16,2,3,17,4,12,7,2,10,18,3,2,11,8,3,5,6,2,14,12,4,5,3,8,15,2,19,9,20,2,7,2,6,17
%N A339874 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A052126(n) for n > 1, and f(1) = 0.
%C A339874 For all i, j:
%C A339874   A305800(i) = A305800(j) => a(i) = a(j),
%C A339874   a(i) = a(j) => A001222(i) = A001222(j),
%C A339874   a(i) = a(j) => A322826(i) = A322826(j).
%H A339874 Antti Karttunen, <a href="/A339874/b339874.txt">Table of n, a(n) for n = 1..65537</a>
%F A339874 a(1) = 1; for n > 1, a(n) = 1 + A322826(n).
%o A339874 (PARI)
%o A339874 up_to = 65537;
%o A339874 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 A339874 A052126(n) = if(1==n,n,(n/vecmax(factor(n)[, 1])));
%o A339874 Aux339874(n) = if(1==n,0,A052126(n));
%o A339874 v339874 = rgs_transform(vector(up_to, n, Aux339874(n)));
%o A339874 A339874(n) = v339874[n];
%Y A339874 Cf. A052126, A322826.
%Y A339874 Cf. also A305800, A300226, A334107, A334108.
%K A339874 nonn
%O A339874 1,2
%A A339874 _Antti Karttunen_, Dec 25 2020