experimental-projects/oeis-research/Altug Alkan/a(n) is the smallest k such that usigma(k) = primorial(n)/upper-bounds.sf

#!/usr/bin/ruby

# a(n) is the smallest k such that usigma(k) = A002110(n), or 0 if no such k exists.
# https://oeis.org/A291356

# Some upper-bounds:
#   a(23) <= ? (probably 0)
#   a(24) <= 15845827930897033847100358400905538
#   a(25) <= 1537045309297012283168734764887837378
#   a(26) <= 225805929074906531781879580005340473248
#   a(27) <= ? (probably 0)
#   a(28) <= 2526893408093537885026065541257916699957568

var n = 24
var prim = n.pn_primorial
var nums = squarefree(1, 10000).grep{ .is_smooth(n.prime) }

for k in (nums) {

    var t = (prim/k - 1)

    for v in (1..15) {
        var u = (t << v)
        if (u.usigma == prim) {
            say u
        }
    }
}