A155900 Numbers k such that Omega(k) = Omega(2^k-1), where Omega(k) is the number of prime factors of k counted with multiplicity (A001222).

1, 2, 3, 4, 5, 7, 8, 9, 13, 16, 17, 19, 27, 31, 32, 49, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217

Offset: 1

Author

M. F. Hasler, Feb 01 2009

Keywords

• nonn
• more

Comments

Mersenne prime exponents A000043 are a subsequence, with Omega(p)=Omega(2^p-1)=1.

Links

• Davar55 et al., "Mersenne-Like", discussion on mersenneforum.org, Jan 27 2009.

Crossrefs

Cf. A000043, A000225, A001222, A046051.

Programs

Mathematica

Select[Range[200],PrimeOmega[#]==PrimeOmega[2^#-1]&] (* Harvey P. Dale, Apr 21 2012 *)

PARI

for( i=1,999, bigomega(2^i-1)==bigomega(i) & print1(i","))

Formula

{n: A046051(n) = A001222(n)}. - R. J. Mathar, Mar 14 2009

Extensions

a(21)-a(22) from Amiram Eldar, Feb 23 2021

a(23)-a(26) from Daniel Suteu, Jan 21 2023