A323241 - OEIS

%I #11 Jan 08 2019 19:08:40

%S 1,2,3,4,3,5,3,6,3,5,3,7,3,5,3,8,3,9,3,7,3,5,3,10,3,5,3,7,3,11,3,12,3,

%T 5,3,13,3,5,3,10,3,11,3,7,3,5,3,14,3,15,3,7,3,16,3,10,3,5,3,17,3,5,3,

%U 18,3,11,3,7,3,19,3,20,3,5,3,7,3,11,3,14,3,5,3,17,3,5,3,10,3,21,3,7,3,5,3,22,3,23,3,24,3,11,3,10,3

%N 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 odd number > 1, and f(n) = A300226(n) for even numbers >= 4.

%C For all i, j:

%C   A319701(i) = A319701(j) => a(i) = a(j),

%C   a(i) = a(j) => A007814(i) = A007814(j).

%C   a(i) = a(j) => A183063(i) = A183063(j).

%H Antti Karttunen, <a href="/A323241/b323241.txt">Table of n, a(n) for n = 1..100000</a>

%o (PARI)

%o up_to = 10000;

%o 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 A052126(n) = if(1==n, n, n/vecmax(factor(n)[, 1]));

%o A319988(n) = ((n>1)&&(factor(n)[omega(n),2]>1));

%o A323241aux(n) = if(n<=2,-n,if(n%2,0,[A052126(n), A319988(n)]));

%o v323241 = rgs_transform(vector(up_to,n,A323241aux(n)));

%o A323241(n) = v323241[n];

%Y Cf. A007814, A052126, A183063, A300226, A319701, A319988, A323235, A323237, A323238, A323242.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 07 2019