cp's OEIS Frontend

A337786 Numbers of the form x^3 + x^2*y + x*y^2 + y^3 where x and y are positive integers, but having no such representation where x and y are coprime.

%I A337786 #10 Sep 23 2020 22:30:59
%S A337786 32,108,120,256,320,405,500,520,680,864,960,1080,1248,1372,1400,1624,
%T A337786 1755,1875,2048,2072,2176,2295,2560,2916,2952,3200,3240,3816,4000,
%U A337786 4160,4212,4640,4680,4725,5000,5145,5324,5368,5440,5481,5720,6424,6560,6912,6993,7104,7344,7480,7680,8125,8640
%N A337786 Numbers of the form x^3 + x^2*y + x*y^2 + y^3 where x and y are positive integers, but having no such representation where x and y are coprime.
%C A337786 Complement of A336995 in A336607.
%H A337786 Robert Israel, <a href="/A337786/b337786.txt">Table of n, a(n) for n = 1..10000</a>
%e A337786 a(3)=120 is a member because 120 = x^3 + x^2*y + x*y^2 + y^3 where x=2 and y=4, but has no such representation where x and y are coprime positive integers.
%e A337786 206312 is not a member because although 206312 = x^3 + x^2*y + x*y^2 + y^3 where x=32 and y=42 are not coprime, it also has such a representation where x=15 and y=53 are coprime.
%p A337786 N:= 10000: # for terms <= N
%p A337786 S1:= {}: S2:= {}:
%p A337786 for x from 1 while (x+1)*(x^2+1) < N do
%p A337786    C:= {seq(i,i=1..min(x,(N-x^3)/x^2))}:
%p A337786    C1,C2:= selectremove(y -> igcd(x,y)=1, C);
%p A337786    V1:= select(`<=`,map(y -> (x+y)*(x^2+y^2), C1),N);
%p A337786    V2:=  select(`<=`,map(y -> (x+y)*(x^2+y^2), C2),N);
%p A337786    S1:= S1 union V1;
%p A337786    S2:= S2 union V2;
%p A337786 od:
%p A337786 sort(convert(S2 minus S1,list));
%Y A337786 Cf. A336607, A336995. Contained in A046099.
%K A337786 nonn
%O A337786 1,1
%A A337786 _Robert Israel_, Sep 21 2020