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

1,2

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.

Links

Table of n, a(n) for n=1..71.

Prog

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

Crossrefs

Cf. A117319

Sequence in context: A353442 A140888 A053753 * A090068 A070899 A265756

Adjacent sequences: A228377 A228378 A228379 * A228381 A228382 A228383

Keyword

nonn

Author

Thomas Bokk, Aug 21 2013

Extensions

More terms from Max Alekseyev, Sep 29 2015

Status

approved