Nonhypotenuse number

In mathematics, a nonhypotenuse number is a natural number whose square cannot be written as the sum of two nonzero squares.

The name stems from the fact that an edge of length equal to a nonhypotenuse number cannot form the hypotenuse of a right angle triangle with integer sides.

The first fifty nonhypotenuse numbers are: Although nonhypotenuse numbers are common among small integers, they become more-and-more sparse for larger numbers.

[1] The nonhypotenuse numbers are those numbers that have no prime factors of the form 4k+1.

[2] Equivalently, they are the number that cannot be expressed in the form

A number whose prime factors are not all of the form 4k+1 cannot be the hypotenuse of a primitive integer right triangle (one for which the sides do not have a nontrivial common divisor), but may still be the hypotenuse of a non-primitive triangle.

[3] The nonhypotenuse numbers have been applied to prove the existence of addition chains that compute the first