experimental-projects/oeis-research/Altug Alkan/Least k such that k is the product of n distinct primes and sigma(k) is an n-th power/inverse_sigma.sf

#!/usr/bin/ruby

# Least k such that k is the product of n distinct primes and sigma(k) is an n-th power.
# https://oeis.org/A281140

# a(14) <= 94467020965716904490370

func a(n) {

    for k in (2..1e9) {

        k.is_smooth(3) || next;
        inverse_sigma_len(k**n) <= 2e6 || next

        inverse_sigma(k**n).each {|v|
            if (v.is_squarefree && v.is_almost_prime(n)) {
                return v
            }
        }
    }
}

for n in (1..20) {
    say [n, a(n)]
}

__END__
[1, 2]
[2, 22]
[3, 102]
[4, 510]
[5, 90510]
[6, 995610]
[7, 11616990]
[8, 130258590]
[9, 1483974030]
[10, 18404105922510]
[11, 428454465915630]
[12, 10195374973815570]
[13, 240871269907008510]