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A104494
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Positive integers n such that n^17 + 1 is semiprime (A001358).
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14
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2, 58, 66, 166, 268, 270, 408, 600, 672, 808, 822, 970, 1050, 1090, 1150, 1200, 1212, 1380, 1578, 1752, 1912, 1950, 1986, 2016, 2038, 2292, 2340, 2548, 2590, 2656, 2718, 2800, 2856, 3162, 3300, 3342, 3738, 4138, 4152, 4228, 4270, 4272, 4362, 4782, 5080, 5166
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n)^17 + 1 is semiprime (A001358).
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EXAMPLE
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2^17 + 1 = 131073 = 3 * 43691,
58^17 + 1 = 951208868148684143308060622849 = 59 * 16122184205909900734034925811,
66^17 + 1 = 8555529718761317069203003539457 = 67 * 127694473414348015958253784171,
1050^17 + 1 = 2292018317801032401637344360351562500000000000000001 = 1051 * 2180797638250268698037435166842590390104662226451.
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MATHEMATICA
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Select[Range[1000000], PrimeQ[# + 1] && PrimeQ[(#^17 + 1)/(# + 1)] &] (* Robert Price, Mar 10 2015 *)
Select[Range[5200], PrimeOmega[#^17+1]==2&] (* Harvey P. Dale, Mar 07 2017 *)
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PROG
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(PARI) for(n=1, 3000, if(!ispseudoprime(n^17+1), forprime(p=1, 10^4, if((n^17+1)%p==0, if(ispseudoprime((n^17+1)/p), print1(n, ", ")); break)))) \\ Derek Orr, Mar 09 2015
(Magma) IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [n: n in [1..1200]|IsSemiprime(n^17+1)]; // Vincenzo Librandi, Mar 10 2015
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CROSSREFS
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Cf. A001358, A006313, A103854, A104238, A104335, A105041, A105066, A105078, A105122, A105142, A105237, A104479.
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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