sidef-scripts/Math/smallest_k-gonal_inverse.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# Date: 08 March 2018
# https://github.com/trizen

# Given an integer `n`, find the smallest integer k>=3 such that `n` is a k-gonal number.

# Example:
#  a(12) = 5 since 12 is a pentagonal number, but not a square or triangular.

# See also:
#   https://oeis.org/A176774

func smallest_k_gonal_inverse (n) {

    var divisors = (2*n).divisors

    divisors.shift
    divisors.pop

    divisors.reverse.each { |d|

        var t = (d - 1)
        var k = (2*n / d + 2*d - 4)

        if (t `divides` k) {
            var z = k/t

            if (z>2 && z<n) {
                return k/t
            }
        }
    }

    return n
}

for n in (4000 .. 4030) {
    say "a(#{n}) = #{smallest_k_gonal_inverse(n)}"
}