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%I #7 Jul 11 2019 15:47:54
%S 1,2,3,3,3,4,3,5,6,7,3,8,3,9,3,3,3,10,3,11,3,12,3,13,3,14,3,15,3,16,3,
%T 17,3,18,3,19,3,20,3,21,3,22,3,23,24,25,3,26,3,27,3,28,3,29,3,30,3,31,
%U 3,32,3,33,34,3,3,35,3,36,3,37,3,38,3,39,40,41,3,42,3,43,3,44,3,45,3,46,3,47,3,48,3,49,3,50,3,51,3,52,53,3,3,54,3,55,3
%N Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n > 1 and gcd(n,A000005(n)) = 1, with f(n) = n for all other numbers.
%C For all i, j:
%C A305801(i) = A305801(j) => a(i) = a(j),
%C a(i) = a(j) => A009191(i) = A009191(j) => A322980(i) = A322980(j).
%H Antti Karttunen, <a href="/A326201/b326201.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 Aux326201(n) = if((n>1) && (1==gcd(n,numdiv(n))),0,n);
%o v326201 = rgs_transform(vector(up_to, n, Aux326201(n)));
%o A326201(n) = v326201[n];
%Y Cf. A000005, A009191, A046642, A305801, A322980.
%Y Cf. also A326202, A326203.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jul 11 2019
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