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A104494 Positive integers n such that n^17 + 1 is semiprime (A001358).

%I A104494 #25 Sep 08 2022 08:45:17
%S A104494 2,58,66,166,268,270,408,600,672,808,822,970,1050,1090,1150,1200,1212,
%T A104494 1380,1578,1752,1912,1950,1986,2016,2038,2292,2340,2548,2590,2656,
%U A104494 2718,2800,2856,3162,3300,3342,3738,4138,4152,4228,4270,4272,4362,4782,5080,5166
%N A104494 Positive integers n such that n^17 + 1 is semiprime (A001358).
%H A104494 Robert Price, <a href="/A104494/b104494.txt">Table of n, a(n) for n = 1..1000</a>
%F A104494 a(n)^17 + 1 is semiprime (A001358).
%e A104494 2^17 + 1 = 131073 = 3 * 43691,
%e A104494 58^17 + 1 = 951208868148684143308060622849 = 59 * 16122184205909900734034925811,
%e A104494 66^17 + 1 = 8555529718761317069203003539457 = 67 * 127694473414348015958253784171,
%e A104494 1050^17 + 1 = 2292018317801032401637344360351562500000000000000001 = 1051 * 2180797638250268698037435166842590390104662226451.
%t A104494 Select[Range[1000000], PrimeQ[# + 1] && PrimeQ[(#^17 + 1)/(# + 1)] &] (* _Robert Price_, Mar 10 2015 *)
%t A104494 Select[Range[5200],PrimeOmega[#^17+1]==2&] (* _Harvey P. Dale_, Mar 07 2017 *)
%o A104494 (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
%o A104494 (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
%Y A104494 Cf. A001358, A006313, A103854, A104238, A104335, A105041, A105066, A105078, A105122, A105142, A105237, A104479.
%K A104494 easy,nonn
%O A104494 1,1
%A A104494 _Jonathan Vos Post_, Apr 19 2005
%E A104494 a(14)-a(46) from _Robert Price_, Mar 09 2015