harmonic_numbers_from_powers_simple.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# License: GPLv3
# Date: 29 July 2017
# https://github.com/trizen

# Computation of the nth-harmonic number, using perfect powers.

func harmonic_numbers_from_powers(n) {

    var seen = []
    var harm = (n <= 0 ? 0 : 1)

    for k in (2 .. n) {
        var p = perfect_root(k)

        if (!seen.exists(p)) {
            var g = p**n.ilog(p)
            harm += ((g-1) // (p-1) / g)
            seen[p] = nil
        }
    }

    return harm
}

for n in (0 .. 30) {
    printf("%20s / %-20s\n", harmonic_numbers_from_powers(n).nude)
}