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A323242 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n<=2) = -n, f(n) = 0 if n is an even number > 2, and f(n) = A300226(n) for odd numbers >= 3.

%I A323242 #6 Jan 08 2019 19:08:46
%S A323242 1,2,3,4,3,4,3,4,5,4,3,4,3,4,6,4,3,4,3,4,6,4,3,4,7,4,8,4,3,4,3,4,6,4,
%T A323242 9,4,3,4,6,4,3,4,3,4,10,4,3,4,11,4,6,4,3,4,9,4,6,4,3,4,3,4,10,4,9,4,3,
%U A323242 4,6,4,3,4,3,4,12,4,13,4,3,4,14,4,3,4,9,4,6,4,3,4,13,4,6,4,9,4,3,4,10,4,3,4,3,4,15
%N A323242 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n<=2) = -n, f(n) = 0 if n is an even number > 2, and f(n) = A300226(n) for odd numbers >= 3.
%H A323242 Antti Karttunen, <a href="/A323242/b323242.txt">Table of n, a(n) for n = 1..100000</a>
%o A323242 (PARI)
%o A323242 up_to = 10000;
%o A323242 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 A323242 A052126(n) = if(1==n, n, n/vecmax(factor(n)[, 1]));
%o A323242 A319988(n) = ((n>1)&&(factor(n)[omega(n),2]>1));
%o A323242 A323242aux(n) = if(n<=2,-n,if(!(n%2),0,[A052126(n), A319988(n)]));
%o A323242 v323242 = rgs_transform(vector(up_to,n,A323242aux(n)));
%o A323242 A323242(n) = v323242[n];
%Y A323242 Cf. A052126, A300226, A319701, A319988, A323241.
%K A323242 nonn
%O A323242 1,2
%A A323242 _Antti Karttunen_, Jan 07 2019