

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.


1



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
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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, (Nx^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



