A257642 Positive integers N such that there is a triangle with rational sides having area and perimeter both equal N.

21, 24, 26, 27, 28, 30, 31, 33, 35, 36, 37, 39, 42, 43, 45, 47, 50, 51, 52, 55, 56, 58, 60, 61, 62, 63, 64, 66, 67, 71, 74, 75, 76, 77, 79, 81, 83, 85, 86, 88, 90, 91, 93, 94, 95, 96, 98, 99, 100, 102, 103, 105, 106, 107, 108, 109, 110, 112, 113, 115, 116, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 137, 138, 141, 143, 145, 147, 148, 149, 150

Offset

1,1

Comments

A positive integer N is in the sequence if and only if there exist positive rational numbers x,y such that x*y>1 and 4*x*y*(x+y)/(x*y-1)=N.

Except for N=27, a positive integer N is in this sequence if and only if N>20 and the elliptic curve w^2 = u^3 + N^2*(u+64)^2 has positive rank.

Links

Table of n, a(n) for n=1..84.

Crossrefs

Cf. A135412, A206334, A228914, A117319, A228380.

Sequence in context: A302679 A302514 A303313 * A332922 A066867 A111356

Adjacent sequences: A257639 A257640 A257641 * A257643 A257644 A257645

Keyword

nonn

Author

Thomas Bokk, Nov 05 2015

Status

approved