A144671 Numbers n such that omega(n) = omega(2^n-1), where omega = A001221 = number of distinct prime factors.

1, 2, 3, 5, 6, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607

Offset: 1

Author

M. F. Hasler, Feb 01 2009

Keywords

• more
• nonn

Comments

A prime p is in this sequence iff 2^p-1 is prime, thus iff p is in A000043 (Mersenne prime exponents), which is a subsequence of this one - and of A155990. The latter contains (some) powers of primes, which cannot be the case here.

Examples

			a(1) = 1 is in this sequence since omega(1) = 0 = omega(2^1-1). Elements of A000043 are primes p such that 2^p-1, they are in this sequence since omega(p) = 1 = omega(2^p-1). a(5) = 6 is in this sequence since omega(6) = #{2,3} = 2 = omega(2^6-1) = #{3,7}.
		

Programs

Mathematica

Select[Range[700],PrimeNu[#]==PrimeNu[2^#-1]&] (* Harvey P. Dale, Jan 04 2018 *)

PARI

is_A144671(n)={ omega(n)==omega(2^n-1) }

Extensions

Two more terms from Max Alekseyev, Apr 27 2010