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A097269
Numbers that are the sum of two nonzero squares but not the difference of two nonzero squares.
14
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
1,1
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
LINKS
Eric Weisstein's World of Mathematics, Sum of Squares Function.
EXAMPLE
2 = 1^2 + 1^2, 10 = 1^2 + 3^2, 18 = 3^2 + 3^2.
PROG
(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
CROSSREFS
Cf. A000404, A024352, A097268, A097270, A097271. Equals twice A057653.
Sequence in context: A069081 A126005 A017089 * A304054 A028413 A282226
KEYWORD
nonn
AUTHOR
Ray Chandler, Aug 19 2004
STATUS
approved