A165564 Numbers which are not congruent numbers, i.e., positive integers which are not the area of any right triangle with rational sides.

1, 2, 3, 4, 8, 9, 10, 11, 12, 16, 17, 18, 19, 25, 26, 27, 32, 33, 35, 36, 40, 42, 43, 44, 48, 49, 50, 51, 57, 58, 59, 64, 66, 67, 68, 72, 73, 74, 75, 76, 81, 82, 83, 89, 90, 91, 97, 98, 99, 100, 104, 105, 106, 107, 108, 113, 114, 115, 121, 122, 123, 128, 129, 130

Offset: 1

Author

Jose Brox (brox(AT)agt.cie.uma.es), Sep 22 2009

Keywords

• nonn

Comments

It is known that every positive integer is the area of some triangle with rational sides. See the survey by Top and Yui. - Jonathan Sondow, Nov 15 2017

References

• Alter, Ronald; Curtz, Thaddeus B.; Kubota, K. K. Remarks and results on congruent numbers. Proceedings of the Third Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1972), pp. 27-35. Florida Atlantic Univ., Boca Raton, Fla., 1972. MR0349554 (50 #2047). - From N. J. A. Sloane, Apr 28 2012

Links

• Michel Marcus, Table of n, a(n) for n = 1..4258
• Boris Iskra, Non-congruent numbers with arbitrarily many prime factors congruent to 3 modulo 8, Proc. Japan Acad. Ser. A Math. Sci., Volume 72, Number 7 (1996), 168-169.
• J. Top and N. Yui, Congruent number problems and their variants, Mathematical Sciences Research Institute Publications, 44 (2008), 613-639.

Crossrefs

Complement of A003273.

Formula

Integers \ { A003273 }.

Extensions

Name corrected by Jonathan Sondow, Nov 15 2017