use strict; use warnings; sub k_almost_prime; for my $k ( 1 .. 5 ) { my $almost = 0; print join(", ", map { 1 until k_almost_prime ++$almost, $k; "$almost"; } 1 .. 10), "\n"; } sub nth_prime; sub k_almost_prime { my ($n, $k) = @_; return if $n <= 1 or $k < 1; my $which_prime = 0; for my $count ( 1 .. $k ) { while( $n % nth_prime $which_prime ) { ++$which_prime; } $n /= nth_prime $which_prime; return if $n == 1 and $count != $k; } ($n == 1) ? 1 : (); } BEGIN { # This is loosely based on one of the python solutions # to the RC Sieve of Eratosthenes task. my @primes = (2, 3, 5, 7); my $p_iter = 1; my $p = $primes[$p_iter]; my $q = $p*$p; my %sieve; my $candidate = $primes[-1] + 2; sub nth_prime { my $n = shift; return if $n < 0; OUTER: while( $#primes < $n ) { while( my $s = delete $sieve{$candidate} ) { my $next = $s + $candidate; $next += $s while exists $sieve{$next}; $sieve{$next} = $s; $candidate += 2; } while( $candidate < $q ) { push @primes, $candidate; $candidate += 2; next OUTER if exists $sieve{$candidate}; } my $twop = 2 * $p; my $next = $q + $twop; $next += $twop while exists $sieve{$next}; $sieve{$next} = $twop; $p = $primes[++$p_iter]; $q = $p * $p; $candidate += 2; } return $primes[$n]; } }