prog.sf

#!/usr/bin/ruby

# a(n) is the least number k such that P(k)^n | k and P(k+1)^n | (k+1), where P(k) = A006530(k) is the largest prime dividing k, or -1 if no such k exists.
# https://oeis.org/A354567

# Known terms:
#   1, 8, 6859, 11859210

# Known upper-bounds:
#   a(5) <= 437489361912143559513287483711091603378 (De Koninck, 2009).

var n = 6

var plimit = 10000
var klimit = 20

var primes = plimit.primes
#var primes = [4957, 6619]

say ":: Searching for a(#{n}) with max(p) = #{plimit} -- cost: ~10^#{primes.len**2 * klimit -> log10.round(-3)}"

primes.each {|p|
    var pn = ipow(p, n)
    primes.each {|q|

        next if (p == q)
        var qn = ipow(q, n)

        var c = Math.chinese([0, pn], [-1, qn])
        var m = (pn * qn)

        for k in (0..klimit) {
            var t = (m*k + c)

            if (t.is_smooth(p) && t.inc.is_smooth(q)) {
                say "[#{k}] Found: a(#{n}) <= #{t}"
            }
        }
    }
}