experimental-projects/oeis-research/Michel Marcus/Smallest m such that gcd of the x's that satisfy sigma(x) = m is n/comb.sf

#!/usr/bin/ruby

# Smallest number m such that the GCD of the x's that satisfy sigma(x)=m is n.
# https://oeis.org/A241625

# Known terms:
#   1, 3, 4, 7, 6, 6187272, 8, 15, 13, 196602, 8105688, 28, 14

# Upper-bounds for a(144):
#   a(144) <= {5334186182, 320692161764, 404350986572, 724592550812, 921030858722, 1138698021812, 7340065485194, 10562405788532, 405101345685452, 1058995989058904, 1293672253540082, 1991013491138282, 2643933035123354, 15645437418062582}

#var easy = Set( 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 18, 19, 22, 27, 29, 32, 36, 37, 43, 45, 49, 50, 61, 64, 67, 72, 73, 81, 91, 98, 100, 101, 106, 109, 121, 128, 129, 133, 134, 137, 146, 148, 149, 152, 157, 162, 163, 169, 171, 173, 192, 193, 197, 199, 200, 202, 211, 217, 218, 219)

func a(n, from=1) {

    for k in (from .. 1e13) {

        say "Testing: #{k}" if (1000 `divides` k)
        var t = k.inverse_sigma.gcd

        if (t == n) {
            return k
        }

        #if ((t > 13) && (t < 200)) {
            #say "a(#{t}) = #{k}" if !easy.has(t)
            #return k if ((t == 14) || (t == 15))
        #}
    }
}

# a(144) <= 921030858722
# a(144) <= 2440369552322

#~ for k in (2..30) {
    #~ say "Tesitng: #{k}"
    #~ for j in (1..4) {
        #~ for i in (1..4){
            #~ var n = (2**k * 31**j * 19**i)
            #~ if (inverse_sigma(n).gcd == 15) {
                #~ die ("Found: ", n)
            #~ }
        #~ }
    #~ }
#~ }


#~ __END__
#var arr = [3, 5, 7, 11, 17, 19, 23, 29, 31, 47, 53, 59, 71, 79, 89, 107, 127, 149, 179, 191, 199, 239, 269]
#var arr = [2, 13, 23, 29, 31, 83, 127, 269, 1153]
#var arr = [2, 3, 5, 7, 13, 17, 19, 97]
#var arr = [2, 3, 5, 7, 11, 17, 31, 71, 127]
var arr = [2, 3, 5, 7, 11, 13, 17, 19, 29, 31, 41, 71, 97, 127, 251, 449, 4801]

for k in (1..30) {
    say "Testing: #{k}"
    arr.combinations_with_repetition(k, {|*a|

        if (a.prod > 1e9) {
            if (inverse_sigma(a.prod).gcd ~~ [14,15,144]) {
                say (a.prod)
            }
        }
    })
}

#say a(144)

#say a(14,1000341000)
#for k in (6..100) {
#    say ("a(#{k}) = ", a(k))
#}
#10000.range.map{.inverse_totient.gcd}.uniq.sort.grep{.is_prime}.say

#~ var table = Hash()

#~ for k in (1..1e4) {
    #~ var t = k.inverse_totient.gcd

    #~ if (!table.has(t)) {
        #~ table{t} = k
    #~ }
#~ }

#~ say table.keys.map{.to_i}.sort.map{table{_}}