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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 21 03:58 EST 2022. Contains 350473 sequences. (Running on oeis4.)