cp's OEIS Frontend

A300231 Filter sequence combining A001065(n) and A009194(n), the sum of proper divisors of n and gcd(n,sigma(n)).

%I A300231 #7 Mar 01 2018 14:53:13
%S A300231 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 A300231 21,2,22,23,24,19,25,2,13,26,27,2,28,2,29,30,31,2,32,33,34,12,35,2,36,
%U A300231 26,37,38,39,2,40,2,41,42,43,44,45,2,46,47,48,2,49,2,50,51,52,44,53,2,54,55,56,2,57,38,35,30,58,2,59,60,32,61,62,63,64
%N A300231 Filter sequence combining A001065(n) and A009194(n), the sum of proper divisors of n and gcd(n,sigma(n)).
%C A300231 Restricted growth sequence transform of P(A001065(n), A009194(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.
%H A300231 Antti Karttunen, <a href="/A300231/b300231.txt">Table of n, a(n) for n = 1..65537</a>
%e A300231 a(27) = a(35) (= 19) because A001065(27) = A001065(35) = 13 and A009194(27) = A009194(35) = 1.
%o A300231 (PARI)
%o A300231 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 A300231 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A300231 A001065(n) = (sigma(n)-n);
%o A300231 A009194(n) = gcd(n, sigma(n));
%o A300231 Aux300231(n) = (1/2)*(2 + ((A001065(n)+A009194(n))^2) - A001065(n) - 3*A009194(n));
%o A300231 write_to_bfile(1,rgs_transform(vector(65537,n,Aux300231(n))),"b300231.txt");
%Y A300231 Cf. A001065, A009194.
%Y A300231 Cf. also A295885, A300223, A300226, A300229, A300230, A300232, A300233, A300235.
%K A300231 nonn
%O A300231 1,2
%A A300231 _Antti Karttunen_, Mar 01 2018