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A300240 Filter sequence combining A009195(n) and A046523(n), i.e., gcd(n,phi(n)) and the prime signature of n.

%I A300240 #7 Mar 02 2018 22:45:20
%S A300240 1,2,2,3,2,4,2,5,6,4,2,7,2,4,8,9,2,10,2,7,11,4,2,12,13,4,14,7,2,15,2,
%T A300240 16,8,4,8,17,2,4,11,12,2,18,2,7,19,4,2,20,21,22,8,7,2,23,24,12,11,4,2,
%U A300240 25,2,4,26,27,8,15,2,7,8,15,2,28,2,4,29,7,8,18,2,20,30,4,2,31,8,4,8,12,2,32,8,7,11,4,8,33,2,34,19,35,2,15,2,12,36
%N A300240 Filter sequence combining A009195(n) and A046523(n), i.e., gcd(n,phi(n)) and the prime signature of n.
%C A300240 Restricted growth sequence transform of P(A009195(n), A046523(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.
%H A300240 Antti Karttunen, <a href="/A300240/b300240.txt">Table of n, a(n) for n = 1..65537</a>
%e A300240 a(6) = a(10) (= 4) because both 6 and 10 are nonsquare semiprimes, and A009195(6) = A009195(10) = 2.
%o A300240 (PARI)
%o A300240 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 A300240 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A300240 A009195(n) = gcd(n, eulerphi(n));
%o A300240 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A300240 Aux300240(n) = (1/2)*(2 + ((A046523(n)+A009195(n))^2) - A046523(n) - 3*A009195(n));
%o A300240 write_to_bfile(1,rgs_transform(vector(65537,n,Aux300240(n))),"b300240.txt");
%Y A300240 Cf. A009195, A046523.
%Y A300240 Cf. also A300230, A300241, A300242, A300243.
%K A300240 nonn
%O A300240 1,2
%A A300240 _Antti Karttunen_, Mar 02 2018