A323374 - OEIS

%I #7 Jan 13 2019 19:29:49

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

%T 16,12,16,17,13,3,18,17,16,3,13,3,19,20,21,3,16,22,19,23,24,3,18,25,

%U 26,27,28,3,16,3,29,30,31,32,33,3,31,34,24,3,26,3,35,25,36,37,26,3,31,38,39,3,26,40,41,42,39,3,26,43,44,37,45,46,31,3,41,47,39,3,31,3,48

%N Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = A323373(n) for all other numbers, except f(p) = -(p mod 2) for primes p.

%C For all i, j:

%C   A305801(i) = A305801(j) => a(i) = a(j),

%C   a(i) = a(j) => A039651(i) = A039651(j).

%H Antti Karttunen, <a href="/A323374/b323374.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 A049559(n) = gcd(eulerphi(n), n-1);

%o A160595(n) = if(1==n, n, numerator(eulerphi(n)/(n-1)));

%o Aux323374(n) = if(isprime(n),-(n%2),[A049559(n), A160595(n)]);

%o v323374 = rgs_transform(vector(up_to, n, Aux323374(n)));

%o A323374(n) = v323374[n];

%Y Cf. A039651, A049559, A160595, A323373.

%Y Cf. also A322587, A322592, A323405.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 13 2019