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A085724
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Numbers n such that 2^n - 1 is a semiprime (A001358).
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14
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4, 9, 11, 23, 37, 41, 49, 59, 67, 83, 97, 101, 103, 109, 131, 137, 139, 149, 167, 197, 199, 227, 241, 269, 271, 281, 293, 347, 373, 379, 421, 457, 487, 523, 727, 809, 881, 971, 983, 997, 1061, 1063
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OFFSET
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1,1
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COMMENTS
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1427 and 1487 are also terms. 1277 is the only remaining unknown below them. - Charles R Greathouse IV, Jun 05 2013
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
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REFERENCES
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J. Earls, Mathematical Bliss, Pleroma Publications, 2009, pages 56-60. ASIN: B002ACVZ6O [From Jason Earls, Nov 22 2009]
J. Earls, "Cole Semiprimes," Mathematical Bliss, Pleroma Publications, 2009, pages 56-60. ASIN: B002ACVZ6O [From Jason Earls, Nov 25 2009]
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LINKS
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Eric Weisstein's World of Mathematics, Semiprime
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EXAMPLE
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11 is a member because 2^11 - 1 = 23*89.
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MATHEMATICA
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SemiPrimeQ[n_]:=(n>1) && (2==Plus@@(Transpose[FactorInteger[n]][[2]])); Select[Range[100], SemiPrimeQ[2^#-1]&] (Noe)
Select[Range[1100], PrimeOmega[2^#-1]==2&] (* Harvey P. Dale, Feb 18 2018 *)
Select[Range[250], Total[Last /@ FactorInteger[2^# - 1, 3]] == 2 &] (* Eric W. Weisstein, Jul 28 2022 *)
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PROG
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(PARI) issemi(n)=bigomega(n)==2
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
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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More terms from Cunningham project, Mar 23 2004
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STATUS
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approved
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