count_of_pythagorean_triples_with_side_n.sf

#!/usr/bin/ruby

# Formula for counting the number of integer-sided right triangles with n as a hypotenuse or leg.

# See also:
#   https://oeis.org/A046081
#   https://projecteuler.net/problem=827

func count_of_pythagorean_triples(n) {

    # Inspired by the PARI/GP program by Michel Marcus, Mar 07 2016.
    # https://oeis.org/A046081

    var n0_sigma0 = 1
    var n1_sigma0 = 1

    for p,e in (n.factor_exp) {
        if (p == 2) {
            n0_sigma0 *= (2*e - 1)
        }
        else {
            n0_sigma0 *= (2*e + 1)
            if (p % 4 == 1) {
                n1_sigma0 *= (2*e + 1)
            }
        }
    }

    (n0_sigma0 + n1_sigma0)/2 - 1
}

say count_of_pythagorean_triples(48)
say count_of_pythagorean_triples(8064000)

assert_eq(
    1000.of(count_of_pythagorean_triples).slice(1),
    1000.of { .sqr.sum_of_squares.len.dec + .sqr.diff_of_squares.len.dec }.slice(1)
)