A176071 Numbers of the form 2^k + k + 1 that are the product of two distinct primes.

21, 38, 265, 4109, 65553, 262163, 1048597, 67108891, 274877906983, 4503599627370549, 73786976294838206531, 75557863725914323419213, 302231454903657293676623, 5192296858534827628530496329220209, 10889035741470030830827987437816582766726, 95780971304118053647396689196894323976171195136475313

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Apr 07 2010

Keywords

• nonn

Examples

			21 = 3 * 7 = 2^4 + 4 + 1
		

Crossrefs

Cf. A005126, A053698, A061421, A174969, A176069, A176070.

Programs

Mathematica

f[n_]:=Last/@FactorInteger[n]=={1,1};Select[Array[2^#+#+1&,140,0],f[ # ]&]
Select[Table[2^k+k+1,{k,0,200}],PrimeNu[#]==PrimeOmega[#]==2&] (* Harvey P. Dale, Jul 11 2023 *)

PARI

is(n) = my(f = factor(n), e = logint(n, 2)); f[,2] == [1, 1]~ && n == 1<David A. Corneth, May 27 2023

Extensions

Name corrected by David A. Corneth, May 27 2023