A045897 Has both a primitive and imprimitive representation as x^2 + xy + y^2.

49, 147, 169, 343, 361, 507, 637, 931, 961, 1029, 1083, 1183, 1369, 1519, 1813, 1849, 1911, 2107, 2197, 2401, 2527, 2793, 2883, 2989, 3211, 3283, 3549, 3577, 3721, 3871, 4107, 4459, 4489, 4557, 4693, 4753, 5047, 5239, 5329, 5341, 5439, 5547, 6223, 6241

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			49 = 7^2 = 5^2 + 5*3 + 3^2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to A2 = hexagonal = triangular lattice

Crossrefs

Intersection of A034017 and A034019.

Cf. A004611, A003136.

Programs

PARI

is(n)=my(f=factor(n), t); for(i=1, #f~, if(f[i, 1]%3!=1 && (f[i, 1]!=3 || f[i, 2]>1), return(0)); if(f[i, 1]%3<2 && f[i, 2]>1, t=1); if(f[i, 1]%3==2, if(f[i, 2]%2, return(0), t=1))); t \\ Charles R Greathouse IV, Nov 04 2015

Extensions

Extended by Ray Chandler, Jan 29 2009