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A228914 Positive integers N such that 1/N = p/q - q/p + r/s - s/r for some positive integers p,q,r,s. 1

%I #15 Dec 30 2015 15:03:02

%S 4,5,9,12,15,20,21,22,24,26,29,30,31,32,34,35,36,37,38,40,43,44,53,55,

%T 56,58,59,60,62,64,66,67,68,69,70,71,74,76,77,80,82,84,86,87,88,90,91,

%U 92,94,95,102,103,104,105,106,108,109,110,112,113,115,117,122,123,129,131,132,133,135,136,137,138,139,140,141,143,144,147

%N Positive integers N such that 1/N = p/q - q/p + r/s - s/r for some positive integers p,q,r,s.

%C Positive integer N belongs to this sequence if and only if the elliptic curve y^2 = x^3 + (8*N^2+1)*x^2 + 16*N^4*x has positive rank.

%o (PARI) { isA228914(n) = ellanalyticrank(ellinit([0, 8*n^2+1, 0, 16*n^4, 0]))[1]; } /* _Max Alekseyev_, Dec 30 2015 */

%Y Cf. A206334, A228380

%K nonn

%O 1,1

%A _Thomas Bokk_, Sep 13 2013

%E More terms from _Max Alekseyev_, Sep 13 2013

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Last modified August 27 16:23 EDT 2024. Contains 375470 sequences. (Running on oeis4.)