is_almost_prime.sf

#!/usr/bin/ruby

# Least number k such that k^n and k^n-1 contain the same number of prime factors (counted with multiplicity) or 0 if no such k exists.
# https://oeis.org/A241793

# Known terms:
#   3, 34, 5, 15, 17, 55, 79, 5, 53, 23, 337, 13, 601, 79, 241, 41, 18433, 31, 40961, 89, 3313, 1153

# New terms:
#   a(23) = 286721
#   a(24) = 79
#   a(25) = ?
#   a(26) = 15937
#   a(27) = 23041
#   a(28) = 1693

# Lower-bounds:
#   a(23) > 239328
#   a(25) > 57600
#   a(29) > 65536

# Upper-bounds:
#   a(23) <= 286721. - Jon E. Schoenfield, Sep 25 2018

Num!VERBOSE = true

func a(m, from=2) {
    for k in (from..Inf) {

        var n = bigomega(k)*m
        var v = (k**m - 1)

        say "[#{m}] Checking: #{k}^#{m}-1 for n = #{n}"

        if (v.is_almost_prime(n)) {
            return k
        }
    }
}

var from = 57600

for n in (25) {
    say "a(#{n}) = #{a(n, from)}"
}

__END__
for n in (1..100) {
    say "a(#{n}) = #{a(n)}"
}

# Unfactorized candidates:

239329^23-1
239873^23-1 -- disproved
241793^23-1 -- disproved
261761^23-1
269953^23-1 -- disproved
273313^23-1
273457^23-1
274177^23-1
276049^23-1
278017^23-1
280001^23-1
280897^23-1
285841^23-1