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A104494 Positive integers n such that n^17 + 1 is semiprime (A001358). 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

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

EXAMPLE

2^17 + 1 = 131073 = 3 * 43691,

58^17 + 1 = 951208868148684143308060622849 = 59 * 16122184205909900734034925811,

66^17 + 1 = 8555529718761317069203003539457 = 67 * 127694473414348015958253784171,

1050^17 + 1 = 2292018317801032401637344360351562500000000000000001 = 1051 * 2180797638250268698037435166842590390104662226451.

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 *)

PROG

(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

CROSSREFS

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

Sequence in context: A024237 A030263 A090743 * A121931 A156507 A285148

Adjacent sequences:  A104491 A104492 A104493 * A104495 A104496 A104497

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Apr 19 2005

EXTENSIONS

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

STATUS

approved

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Last modified April 11 18:00 EDT 2021. Contains 342888 sequences. (Running on oeis4.)