A097269 Numbers that are the sum of two nonzero squares but not the difference of two nonzero squares.

2, 10, 18, 26, 34, 50, 58, 74, 82, 90, 98, 106, 122, 130, 146, 162, 170, 178, 194, 202, 218, 226, 234, 242, 250, 274, 290, 298, 306, 314, 338, 346, 362, 370, 386, 394, 410, 442, 450, 458, 466, 482, 490, 514, 522, 530, 538, 554, 562, 578, 586, 610, 626, 634

Offset: 1

Author

Ray Chandler, Aug 19 2004

Keywords

• nonn

Comments

Intersection of A000404 (sum of squares) and complement of A024352 (difference of squares).

Numbers of the form 4k+2 = double of an odd number, with the odd number equal to the sum of 2 squares (sequence A057653). - Jean-Christophe Hervé, Oct 24 2015

Numbers that are the sum of two odd squares. - Jean-Christophe Hervé, Oct 25 2015

Examples

			2 = 1^2 + 1^2, 10 = 1^2 + 3^2, 18 = 3^2 + 3^2.
		

Links

• Eric Weisstein's World of Mathematics, Sum of Squares Function.

Crossrefs

Cf. A000404, A024352, A097268, A097270, A097271. Equals twice A057653.

Cf. A020668, A263715.

Programs

PARI

is(n)=if(n%4!=2,return(0)); my(f=factor(n/2)); for(i=1,#f[,1],if(bitand(f[i,2],1)==1&&bitand(f[i,1],3)==3, return(0))); 1 \\ Charles R Greathouse IV, May 31 2013

Python

from itertools import count, islice
from sympy import factorint
def A097269_gen(): # generator of terms
    return filter(lambda n:all(p & 3 != 3 or e & 1 == 0 for p, e in factorint(n//2).items()),count(2,4))
A097269_list = list(islice(A097269_gen(),30)) # Chai Wah Wu, Jun 28 2022