#!/usr/bin/perl

# a(1)=2048. For n>1, a(n) is the LCM of a(n-1) and A140635(a(n-1)).
# https://oeis.org/A351162

# Perl program written by Daniel Suteu, 15 March 2022.

use 5.020;
use warnings;
use experimental qw(signatures);

use ntheory qw(nth_prime divisor_sum);
use Math::AnyNum qw(:overload lcm);

sub smallest_number_with_n_divisors ($threshold, $least_solution = Inf, $k = 1, $max_a = Inf, $solutions = 1, $n = 1) {

    if ($solutions == $threshold) {
        return $n;
    }

    if ($solutions > $threshold) {
        return $least_solution;
    }

    my $p = nth_prime($k);

    for (my $a = 1 ; $a <= $max_a ; ++$a) {
        $n *= $p;
        last if ($n > $least_solution);
        $least_solution = __SUB__->($threshold, $least_solution, $k + 1, $a, $solutions * ($a + 1), $n);
    }

    return $least_solution;
}

my $u = 2048;

say "a(1) = $u";

foreach my $n (2 .. 100) {
    my $sigma0 = divisor_sum($u, 0);
    my $v      = lcm($u, smallest_number_with_n_divisors($sigma0));
    say "a($n) = $v";
    $u = $v;
}