A155900 - OEIS

%I #20 Jan 21 2023 18:01:30

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

%T 2203,2281,3217

%N 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).

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

%H Davar55 et al., <a href="http://www.mersenneforum.org/showthread.php?t=11418">"Mersenne-Like", discussion on mersenneforum.org</a>, Jan 27 2009.

%F {n: A046051(n) = A001222(n)}. - _R. J. Mathar_, Mar 14 2009

%t Select[Range[200],PrimeOmega[#]==PrimeOmega[2^#-1]&] (* _Harvey P. Dale_, Apr 21 2012 *)

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

%Y Cf. A000043, A000225, A001222, A046051.

%K nonn,more

%O 1,2

%A _M. F. Hasler_, Feb 01 2009

%E a(21)-a(22) from _Amiram Eldar_, Feb 23 2021

%E a(23)-a(26) from _Daniel Suteu_, Jan 21 2023