A228380 Positive integers N such that N = (p^2+q^2)*(r^2-s^2)/((p^2-q^2)*(r^2+s^2)) for some positive integers p,q,r,s.

1, 6, 13, 16, 18, 22, 23, 32, 33, 35, 36, 37, 41, 42, 43, 44, 45, 46, 50, 51, 53, 57, 58, 59, 60, 61, 63, 67, 69, 70, 74, 75, 77, 78, 79, 80, 83, 84, 85, 86, 88, 89, 90, 93, 94, 95, 96, 97, 98, 102, 104, 110, 112, 116, 117, 118, 119, 122, 123, 124, 126, 128, 132, 133, 134, 137, 138, 141, 142, 143, 152

Offset: 1

Author

Thomas Bokk, Aug 21 2013

Keywords

• nonn

Comments

Integer N>1 belongs to this sequence if and only if the elliptic curve y^2 = x^3 - (N^2+1)*x^2 + N^2*x has positive rank.

Crossrefs

Cf. A117319

Programs

PARI

{ isA228380(n) = ellanalyticrank(ellinit([0,-(n^2+1),0,n^2,0]))[1]; } /* Max Alekseyev, Sep 29 2015 */

Extensions

More terms from Max Alekseyev, Sep 29 2015