A323079 - OEIS

%I #6 Jan 04 2019 17:37:45

%S 1,2,3,4,3,5,3,6,7,8,3,7,3,9,10,11,3,12,3,10,13,14,3,15,16,17,18,13,3,

%T 19,3,20,21,22,23,18,3,24,25,16,3,26,3,21,27,28,3,29,30,31,32,25,3,33,

%U 34,23,35,36,3,27,3,37,30,38,39,40,3,32,41,42,3,43,3,44,45,35,46,47,3,48,49,50,3,30,51,52,53,34,3,54,55,41,56,57,58,59,3,60,46,45,3,61,3,39

%N Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = -1 if n is an odd prime, and f(n) = A060681(n) for all other numbers.

%C For all i, j:

%C   a(i) = a(j) => A323076(i) = A323076(j),

%C   a(i) = a(j) => A323077(i) = A323077(j).

%H Antti Karttunen, <a href="/A323079/b323079.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o up_to = 65537;

%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 A060681(n) = (n-if(1==n,n,n/vecmin(factor(n)[,1])));

%o A323079aux(n) = if((n>2)&&isprime(n),-1,A060681(n));

%o v323079 = rgs_transform(vector(up_to,n,A323079aux(n)));

%o A323079(n) = v323079[n];

%Y Cf. A060681, A323076, A323077.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 04 2019