experimental-projects/oeis-research/Thomas Ordowski/Divisibility of numerators of harmonic numbers/harmonic_numerator_divisibility.sf

#!/usr/bin/ruby

# Amiram Eldar and Thomas Ordowski, Jul 27 2019:
#   Conjecutre: For n > 2, n divides a(n-2) if and only if n is a prime.
#   Problem: are there primes p > 3 such that p^2 divides a(p-2)?

# Checked up to 1000000.

# See:
#   https://oeis.org/A064169

var from = 1000000
var H    = harmonic(from-2)

for n in (from .. from+1e6) {

    say "Testing: #{n}"

    var (nu,de) = H.nude
    var t = nu-de

    if (n `divides` t) {
        assert(n.is_prime, n)
    }
    else {
        assert(n.is_composite, n)
    }

    if (n.is_prime) {
        if (n*n `divides` t) {
            die "Counter-example: #{n}"
        }
    }

    H += (n-1).inv
}