A326202 - OEIS

%I #8 Jul 11 2019 15:48:04

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

%T 3,16,17,3,3,3,18,3,19,3,20,3,21,22,23,3,24,3,3,25,26,3,27,3,28,3,29,

%U 3,30,3,31,3,3,3,32,3,33,34,35,3,36,3,37,3,38,3,39,3,40,3,41,3,42,3,43,44,45,3,46,47,48,3,49,50,51,3,3,52,3,3,53,3,54,55

%N Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n > 2 and gcd(n,sigma(n)) = 1, with f(n) = n for all other numbers.

%C For all i, j:

%C   A305801(i) = A305801(j) => A324401(i) = A324401(j) => a(i) = a(j),

%C   a(i) = a(j) => A009194(i) = A009194(j) => A325964(i) = A325964(j).

%H Antti Karttunen, <a href="/A326202/b326202.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 Aux326202(n) = if((n>2) && (1==gcd(n,sigma(n))),0,n);

%o v326202 = rgs_transform(vector(up_to, n, Aux326202(n)));

%o A326202(n) = v326202[n];

%Y Cf. A000203, A009194, A014567, A305801, A324401, A325964.

%Y Cf. also A326200, A326201, A326203.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 11 2019