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Positive integers n such that n^8 + 1 is semiprime.
14

%I #14 Nov 19 2018 10:44:57

%S 6,9,10,13,16,18,20,22,26,28,32,33,34,38,42,43,47,50,51,52,53,56,58,

%T 60,66,68,69,70,72,81,84,92,94,98,102,104,110,116,120,134,136,138,144,

%U 145,160,162,164,166,170,172,174,178,185,188,192,196,198,200,204,205,210

%N Positive integers n such that n^8 + 1 is semiprime.

%C n^8 + 1 is an irreducible polynomial over the integers and thus can be prime (1^8+1=2, 2^8+1=257, 4^8+1=65537) as well as semiprime.

%H Vincenzo Librandi, <a href="/A105066/b105066.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n)^8+1 is an element of A001538.

%e 6^8+1 = 1679617 = 17 * 98801,

%e 16^8+1 = 4294967297 = 641 * 6700417,

%e 72^8+1 = 722204136308737 = 12110113 * 59636449 where the two factors have the same number of digits.

%t fQ[n_] := Flatten[ Table[ #[[2]], {1}] & /@ FactorInteger[n]] == {1, 1}; Select[ Range[220], fQ[ #^8 + 1] &] (* _Robert G. Wilson v_, Apr 06 2005 *)

%t Select[Range[300],PrimeOmega[#^8+1]==2&] (* _Harvey P. Dale_, Nov 19 2018 *)

%Y Cf. A000040, A001538, A103854, A104238, A105041.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Apr 05 2005

%E More terms from _Robert G. Wilson v_, Apr 06 2005