A048737 Numbers whose prime divisors consist of primes p such that 2^p-1 is prime.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 28, 30, 31, 32, 34, 35, 36, 38, 39, 40, 42, 45, 48, 49, 50, 51, 52, 54, 56, 57, 60, 61, 62, 63, 64, 65, 68, 70, 72, 75, 76, 78, 80, 81, 84, 85, 89, 90, 91, 93, 95, 96, 98, 100, 102, 104, 105

Offset: 1

Author

J. Lowell

Keywords

• nonn

Comments

Multiplicative closure of A000043. - Charles R Greathouse IV, Feb 21 2013

Examples

			10 = 2 * 5 is a term since both 2 and 5 are Mersenne exponents (A000043).
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000043, A122254, A122260.

Programs

Mathematica

p = Join[{1}, MersennePrimeExponent @ Range[12]]; Select[Range[p[[-1]]], AllTrue[FactorInteger[#][[;; , 1]], MemberQ[p, #] &] &] (* Amiram Eldar, Sep 27 2020 *)

Formula

a(n) = A122254(n) = A122260(n) for n < 22. - Reinhard Zumkeller, Aug 29 2006

Sum_{n>=1} 1/a(n) = Product_{p in A000043} p/(p-1) = 5.7838... - Amiram Eldar, Sep 27 2020

Extensions

More terms from James Sellers, Apr 22 2000