A144482 Semiprimes that are a product of Mersenne primes.

9, 21, 49, 93, 217, 381, 889, 961, 3937, 16129, 24573, 57337, 253921, 393213, 917497, 1040257, 1572861, 3670009, 4063201, 16252897, 16646017, 66584449, 67092481, 1073602561, 4294434817, 6442450941, 15032385529, 17179607041

Offset: 1

Author

G. L. Honaker, Jr., Oct 12 2008

Keywords

• nonn

Comments

As the product of any two primes is semiprime by definition, this is also the list of composite numbers n=x*y where both x and y are Mersenne primes. - Christian N. K. Anderson, Mar 25 2013

Links

• Christian N. K. Anderson, Table of n, a(n) for n = 1..75

Crossrefs

Cf. A000668, A001358, A144856, A333788.

Subsequence of A335882.

Programs

Mathematica

Take[Times@@@Tuples[2^# -1&/@MersennePrimeExponent[Range[10]],2]//Union,30] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 30 2020 *)

PARI

isA000668(n) = (isprime(n)&&!bitand(n,1+n));
isA144482(n) = ((2==bigomega(n))&&isA000668(vecmin(factor(n)[,1]))&&isA000668(vecmax(factor(n)[,1]))); \\ Antti Karttunen, Jun 28 2020