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

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

Offset: 1

Author

Jonathan Vos Post, Apr 19 2005

Keywords

• easy
• nonn

Examples

			2^17 + 1 = 131073 = 3 * 43691,
58^17 + 1 = 951208868148684143308060622849 = 59 * 16122184205909900734034925811,
66^17 + 1 = 8555529718761317069203003539457 = 67 * 127694473414348015958253784171,
1050^17 + 1 = 2292018317801032401637344360351562500000000000000001 = 1051 * 2180797638250268698037435166842590390104662226451.
		

Links

• Robert Price, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001358, A006313, A103854, A104238, A104335, A105041, A105066, A105078, A105122, A105142, A105237, A104479.

Programs

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

Mathematica

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 *)

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

Formula

a(n)^17 + 1 is semiprime (A001358).

Extensions

a(14)-a(46) from Robert Price, Mar 09 2015