cp's OEIS Frontend

A300243 Filter sequence combining A051953(n) and A009195(n), n-phi(n) (cototient of n) and gcd(n,n-phi(n)).

%I A300243 #6 Mar 02 2018 14:15:49
%S A300243 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,18,19,20,2,
%T A300243 21,2,22,23,24,25,26,2,27,28,29,2,30,2,31,32,33,2,34,35,36,37,38,2,39,
%U A300243 40,41,32,42,2,43,2,44,45,46,47,48,2,49,50,48,2,51,2,52,53,54,47,55,2,56,57,58,2,59,60,61,62,63,2,64,37,65,66,67,68,69,2,70,71
%N A300243 Filter sequence combining A051953(n) and A009195(n), n-phi(n) (cototient of n) and gcd(n,n-phi(n)).
%C A300243 Restricted growth sequence transform of P(A051953(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 A300243 Antti Karttunen, <a href="/A300243/b300243.txt">Table of n, a(n) for n = 1..65537</a>
%e A300243 a(66) = a(70) (= 48) because A051953(66) = A051953(70) = 46 and A009195(66) = A009195(70) = 2.
%o A300243 (PARI)
%o A300243 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 A300243 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A300243 A009195(n) = gcd(n, eulerphi(n));
%o A300243 A051953(n) = (n - eulerphi(n));
%o A300243 Aux300243(n) = (1/2)*(2 + ((A051953(n)+A009195(n))^2) - A051953(n) - 3*A009195(n));
%o A300243 write_to_bfile(1,rgs_transform(vector(65537,n,Aux300243(n))),"b300243.txt");
%Y A300243 Cf. A009195, A051953.
%Y A300243 Cf. also A300233, A300240, A300241, A300242.
%K A300243 nonn
%O A300243 1,2
%A A300243 _Antti Karttunen_, Mar 02 2018