experimental-projects/oeis-research/Felix Fröhlich/3-powerful numbers = sum of two coprime 3-powerful numbers/generate.sf

#!/usr/bin/ruby

# 3-powerful numbers that can be written as the sum of two coprime 3-powerful numbers.
# https://oeis.org/A297867

# Knwon terms:
#   776151559, 3518958160000

# Potential values for a:
#   (11*n + 7)^3
#   (12n+7)^3
#   (10*n + 1)^3

# Also of interest may be:
#   https://oeis.org/A277636

func k_powerful_numbers(n, t, k=2) {

    var powerful = []

    func (m,r) {

        if (r < k) {
            if (m > t) {
                powerful << m
            }
            return nil
        }

        for a in (1 .. iroot(idiv(n,m), r)) {

            a.is_coprime(t) || next

            if (r > k) {
                a.is_coprime(m) || next
                a.is_squarefree || next
            }
            __FUNC__(m * a**r, r-1)
        }

    }(1, 2*k - 1)

    powerful
}

#var M = 776151559
#var P = powerful(M, 3).grep { _ > 1e4 }

var P = (1..100 -> map {|n| (11*n + 7)**3 })
#var P = (1..100 -> map {|n| (12*n + 7)**3 })
#var P = (1..100 -> map {|n| (10*n + 1)**3 })

for a in (P) {
    for b in (k_powerful_numbers(100*a, a, 3)) {

        if (is_powerful(a + b, 3)) {
            say "#{a} + #{b} = #{a + b}"
        }

        if (is_powerful(abs(a-b), 3)) {
            say "Found triple: (#{a}, #{b}, #{abs(a-b)})"
        }
    }
}

__END__

Found triple: (19902511, 776151559, 756249048)
19902511 + 756249048 = 776151559