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%I #30 Jul 28 2022 21:15:37
%S 4,9,11,23,37,41,49,59,67,83,97,101,103,109,131,137,139,149,167,197,
%T 199,227,241,269,271,281,293,347,373,379,421,457,487,523,727,809,881,
%U 971,983,997,1061,1063
%N Numbers n such that 2^n - 1 is a semiprime (A001358).
%C Subsequence of A000430. Apart from 4, 9, and 49 composites in this sequence are greater than 1.9e7. - _Charles R Greathouse IV_, Jun 05 2013
%C 1427 and 1487 are also terms. 1277 is the only remaining unknown below them. - _Charles R Greathouse IV_, Jun 05 2013
%C Among the known terms only 11, 23, 83 and 131 are in A002515, that is, they are the only known values for n such that (2^n - 1)/(2*n + 1) is prime. - _Jianing Song_, Jan 22 2019
%D J. Earls, Mathematical Bliss, Pleroma Publications, 2009, pages 56-60. ASIN: B002ACVZ6O [From _Jason Earls_, Nov 22 2009]
%D J. Earls, "Cole Semiprimes," Mathematical Bliss, Pleroma Publications, 2009, pages 56-60. ASIN: B002ACVZ6O [From _Jason Earls_, Nov 25 2009]
%H S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MersenneNumber.html">Mersenne Number</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime</a>
%e 11 is a member because 2^11 - 1 = 23*89.
%t SemiPrimeQ[n_]:=(n>1) && (2==Plus@@(Transpose[FactorInteger[n]][[2]])); Select[Range[100],SemiPrimeQ[2^#-1]&] (Noe)
%t Select[Range[1100],PrimeOmega[2^#-1]==2&] (* _Harvey P. Dale_, Feb 18 2018 *)
%t Select[Range[250], Total[Last /@ FactorInteger[2^# - 1, 3]] == 2 &] (* _Eric W. Weisstein_, Jul 28 2022 *)
%o (PARI) issemi(n)=bigomega(n)==2
%o is(n)=if(isprime(n), issemi(2^n-1), my(q); isprimepower(n,&q)==2 && ispseudoprime(2^q-1) && ispseudoprime((2^n-1)/(2^q-1))) \\ _Charles R Greathouse IV_, Jun 05 2013
%Y Cf. A092558, A092559, A092561, A092562.
%K nonn,more
%O 1,1
%A _Jason Earls_, Jul 20 2003
%E More terms from _Zak Seidov_, Feb 27 2004
%E More terms from Cunningham project, Mar 23 2004
%E More terms from the Cunningham project sent by _Robert G. Wilson v_ and _T. D. Noe_, Feb 22 2006
%E a(41)-a(42) from _Charles R Greathouse IV_, Jun 05 2013
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