sidef-scripts/Math/smallest_number_with_at_least_n_divisors.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# Date: 15 May 2021
# https://github.com/trizen

# Generate the smallest number that has at least n divisors.

# See also:
#   https://oeis.org/A061799 -- Smallest number with at least n divisors.

func smallest_number_with_at_least_n_divisors(threshold, least_solution = Inf, k = 1, max_a = Inf, solutions = 1, n = 1) {

    if (solutions >= threshold) {
        return n
    }

    var p = k.prime

    for a in (1 .. max_a) {
        n *= p
        break if (n > least_solution)
        least_solution = __FUNC__(threshold, least_solution, k+1, a, solutions * (a + 1), n)
    }

    return least_solution
}

say smallest_number_with_at_least_n_divisors(60)     #=> 5040
say smallest_number_with_at_least_n_divisors(1000)   #=> 245044800