Data commit

Task/Untouchable-numbers/Perl/untouchable-numbers.pl

@@ -0,0 +1,37 @@
+use strict;
+use warnings;
+use enum qw(False True);
+use ntheory qw/divisor_sum is_prime/;
+
+sub sieve {
+    my($n) = @_;
+    my %s;
+    for my $k (0 .. $n+1) {
+        my $sum = divisor_sum($k) - $k;
+        $s{$sum} = True if $sum <= $n+1;
+    }
+    %s
+}
+
+my(%s,%c);
+my($max, $limit, $cnt) = (2000, 1e5, 0);
+
+%s = sieve 14 * $limit;
+!is_prime($_) and $c{$_} = True for 1..$limit;
+my @untouchable = (2, 5);
+for ( my $n = 6; $n <= $limit; $n += 2 ) {
+   push @untouchable, $n if !$s{$n} and $c{$n-1} and $c{$n-3};
+}
+map { $cnt++ if $_ <= $max } @untouchable;
+print "Number of untouchable numbers ≤ $max : $cnt \n\n" .
+      (sprintf "@{['%6d' x $cnt]}", @untouchable[0..$cnt-1]) =~ s/(.{84})/$1\n/gr .  "\n";
+
+my($p, $count) = (10, 0);
+my $fmt = "%6d untouchable numbers were found  ≤ %7d\n";
+for my $n (@untouchable) {
+   $count++;
+   if ($n > $p) {
+      printf $fmt, $count-1, $p;
+      printf($fmt, scalar @untouchable, $limit) and last if $limit == ($p *= 10)
+   }
+}