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
Keywords
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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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));
Comments