prop_sigma.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# Date: 16 August 2019
# https://github.com/trizen

# Generate all the divisors d of n, such that d <= k.

# Aliquot sequence starting at 276.
# https://oeis.org/A008892

func divisors_le (n, k) {

    var d  = [1]
    var pp = [
        [2,1],
        [3,2],
        [97,1],
        [197,1],
        [75081990941 ,1],
        [88493269493,1]
        [1384830977701,1]
        [12561733388625059,1]
        [1678129073086710180895595636080546136202087961,1]
        [391364384797113642021018938141302575768663239995535008610511080253072850223856047857018826709557247961017887671,1]
    ]

    assert(pp.all{.first.is_prime})
    assert(pp.prod_2d {|p,k| p**k } == n)

    for p,e in (pp) {
        var r = 1
        d << gather {
            e.times {
                r *= p
                d.each { |u|
                    take(u*r) if (u*r <= k)
                }
            }
        }...
    }

    d.sort
}

var n = 26110157458513265619034078368125391068700794099058184847372911035083675260156495372381837385445470163130669518228029490682124851301249859714720420517651878609243007545569976387750129484086482969920578568241023674

say divisors_le(n,n-1).sum