Super-Poulet numbers

Super-Poulet numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

A super-Poulet number is a Poulet number (or Fermat pseudoprime to base 2) whose every divisor d evenly divides 2^d − 2.

Task

• Find and display the first 20 super-Poulet numbers.

Stretch

• Find and display the index and value of the first super-Poulet number greater than one million.

See also

• Task: Fermat pseudoprimes
• Wikipedia: super-Poulet number
• OEIS:A050217 - super-Poulet numbers

Raku

<lang perl6>use Prime::Factor; use Lingua::EN::Numbers;

my @poulet = lazy (2..*).hyper(:2000batch).grep: { !.is-prime && (1 == expmod 2, $_ - 1, $_) } my @super-poulet = @poulet.grep: { all .&divisors.skip(1).map: { 2 == expmod 2, $_, $_ } }

say "First 20 super-Poulet numbers:\n" ~ @super-poulet[^20].gist;

for 1e6.Int, 1e7.Int -> $threshold {

   say "\nIndex and value of first super-Poulet greater than {$threshold.&cardinal}:";
   my $index = @super-poulet.first: * > $threshold, :k;
   say "{(1+$index).&ordinal-digit} super-Poulet number == " ~ @super-poulet[$index].,

}</lang>

Output:

First 20 super-Poulet numbers:
(341 1387 2047 2701 3277 4033 4369 4681 5461 7957 8321 10261 13747 14491 15709 18721 19951 23377 31417 31609)

Index and value of first super-Poulet greater than one million:
109th super-Poulet number == 1,016,801

Index and value of first super-Poulet greater than ten million:
317th super-Poulet number == 10,031,653