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A176071
Numbers of the form 2^k + k + 1 that are the product of two distinct primes.
0
21, 38, 265, 4109, 65553, 262163, 1048597, 67108891, 274877906983, 4503599627370549, 73786976294838206531, 75557863725914323419213, 302231454903657293676623, 5192296858534827628530496329220209, 10889035741470030830827987437816582766726, 95780971304118053647396689196894323976171195136475313
OFFSET
1,1
EXAMPLE
21 = 3 * 7 = 2^4 + 4 + 1
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 *)
PROG
(PARI) is(n) = my(f = factor(n), e = logint(n, 2)); f[, 2] == [1, 1]~ && n == 1<<e + e + 1 \\ David A. Corneth, May 27 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name corrected by David A. Corneth, May 27 2023
STATUS
approved