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.

32, 108, 120, 256, 320, 405, 500, 520, 680, 864, 960, 1080, 1248, 1372, 1400, 1624, 1755, 1875, 2048, 2072, 2176, 2295, 2560, 2916, 2952, 3200, 3240, 3816, 4000, 4160, 4212, 4640, 4680, 4725, 5000, 5145, 5324, 5368, 5440, 5481, 5720, 6424, 6560, 6912, 6993, 7104, 7344, 7480, 7680, 8125, 8640

Offset

1,1

Comments

Complement of A336995 in A336607.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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.
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.

Maple

N:= 10000: # for terms <= N
S1:= {}: S2:= {}:
for x from 1 while (x+1)*(x^2+1) < N do
   C:= {seq(i, i=1..min(x, (N-x^3)/x^2))}:
   C1, C2:= selectremove(y -> igcd(x, y)=1, C);
   V1:= select(`<=`, map(y -> (x+y)*(x^2+y^2), C1), N);
   V2:=  select(`<=`, map(y -> (x+y)*(x^2+y^2), C2), N);
   S1:= S1 union V1;
   S2:= S2 union V2;
od:
sort(convert(S2 minus S1, list));

Crossrefs

Cf. A336607, A336995. Contained in A046099.

Sequence in context: A063498 A173951 A233691 * A233684 A218068 A333582

Adjacent sequences: A337783 A337784 A337785 * A337787 A337788 A337789

Keyword

nonn

Author

Robert Israel, Sep 21 2020

Status

approved