A226946 Numbers that can't be written as x^2 + x*y + y^2, with 0 <= x <= y and gcd(x,y) = 1.

2, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 80, 81, 82

Offset: 1

Author

Reinhard Zumkeller, Jun 23 2013

Keywords

• nonn

Comments

A000086(a(n)) = 0.

Also numbers n with psi(n) congruent to 0 mod 3, where psi is A001615, and also numbers divisible by 9 or by at least one prime of the form 3k-1: A003627. - Enrique Pérez Herrero, Dec 08 2013

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A034017 (complement).

Cf. A003627, A001615.

Programs

Haskell

a226946 n = a226946_list !! (n-1)
a226946_list = filter ((== 0) . a000086) [1..]
-- Reinhard Zumkeller, Dec 16 2013, Jun 23 2013

Mathematica

Select[Range[1000],Mod[# * Times@@(1+1/Transpose[FactorInteger[#]][[1]]),3]==0&] (* Enrique Pérez Herrero, Dec 08 2013 *)
nn = 10; lim = 1 + nn + nn^2; Complement[Range[2, lim], Select[Union[Flatten[Table[If[GCD[x, y] == 1, x^2 + x*y + y^2, 0], {y, nn}, {x, y}]]], # <= lim &]] (* T. D. Noe, Dec 09 2013 *)

Extensions

The original definition was too weak; thanks to T. D. Noe for having corrected this. - Reinhard Zumkeller, Dec 09 2013