cp's OEIS Frontend

A300242 Filter sequence combining gcd(n,sigma(n)) and gcd(n,phi(n)), (A009194 and A009195).

%I A300242 #6 Mar 02 2018 14:15:57
%S A300242 1,1,1,2,1,3,1,4,5,6,1,7,1,6,8,9,1,10,1,11,5,6,1,12,13,6,14,15,1,3,1,
%T A300242 16,8,6,1,17,1,6,5,18,1,19,1,7,20,6,1,21,22,23,8,11,1,24,13,25,5,6,1,
%U A300242 26,1,6,14,27,1,3,1,11,8,6,1,28,1,6,13,7,1,19,1,29,30,6,1,31,1,6,8,32,1,33,34,7,5,6,35,36,1,37,20,38,1,3,1,39,20
%N A300242 Filter sequence combining gcd(n,sigma(n)) and gcd(n,phi(n)), (A009194 and A009195).
%C A300242 Restricted growth sequence transform of P(A009194(n), A009195(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.
%H A300242 Antti Karttunen, <a href="/A300242/b300242.txt">Table of n, a(n) for n = 1..65537</a>
%e A300242 a(15) = a(33) (= 8) because A009194(15) = A009194(33) = 3 and A009195(15) = A009195(33) = 1.
%e A300242 a(20) = a(52) (= 11) because A009194(20) = A009194(52) = 2 and A009195(20) = A009195(52) = 4.
%o A300242 (PARI)
%o A300242 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 A300242 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A300242 A009194(n) = gcd(n, sigma(n));
%o A300242 A009195(n) = gcd(n, eulerphi(n));
%o A300242 Aux300242(n) = (1/2)*(2 + ((A009194(n)+A009195(n))^2) - A009194(n) - 3*A009195(n));
%o A300242 write_to_bfile(1,rgs_transform(vector(65537,n,Aux300242(n))),"b300242.txt");
%Y A300242 Cf. A009194, A009195.
%Y A300242 Cf. also A286591, A300225, A300240, A300241, A300243.
%K A300242 nonn
%O A300242 1,4
%A A300242 _Antti Karttunen_, Mar 02 2018