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

1,2

Comments

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

Links

Table of n, a(n) for n=1..26.

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000043, A000225, A001222, A046051.

Sequence in context: A192649 A102363 A201816 * A274949 A107684 A111796

Adjacent sequences: A155897 A155898 A155899 * A155901 A155902 A155903

Keyword

nonn,more

Author

M. F. Hasler, Feb 01 2009

Extensions

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

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

Status

approved