cp's OEIS Frontend

A300241 Filter sequence combining A001065(n) and A009195(n), the sum of proper divisors of n and gcd(n,phi(n)).

%I A300241 #6 Mar 02 2018 14:15:26
%S A300241 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 A300241 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 A300241 40,41,42,43,2,44,2,45,46,47,48,49,2,50,51,52,2,53,2,54,55,56,48,57,2,58,59,60,2,61,62,63,64,65,2,66,37,67,68,69,70,71,2,72,73
%N A300241 Filter sequence combining A001065(n) and A009195(n), the sum of proper divisors of n and gcd(n,phi(n)).
%C A300241 Restricted growth sequence transform of P(A001065(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 A300241 Antti Karttunen, <a href="/A300241/b300241.txt">Table of n, a(n) for n = 1..65537</a>
%e A300241 a(65) = a(77) (= 48) because A001065(65) = A001065(77) = 19 and A009195(65) = A009195(77) = 1.
%o A300241 (PARI)
%o A300241 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 A300241 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A300241 A001065(n) = (sigma(n)-n);
%o A300241 A009195(n) = gcd(n, eulerphi(n));
%o A300241 Aux300241(n) = (1/2)*(2 + ((A001065(n)+A009195(n))^2) - A001065(n) - 3*A009195(n));
%o A300241 write_to_bfile(1,rgs_transform(vector(65537,n,Aux300241(n))),"b300241.txt");
%Y A300241 Cf. A001065, A009195.
%Y A300241 Cf. also A300231, A300240, A300242, A300243.
%K A300241 nonn
%O A300241 1,2
%A A300241 _Antti Karttunen_, Mar 02 2018