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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
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
Sequence in context: A030263 A359242 A090743 * A121931 A343578 A156507
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 March 1 14:57 EST 2024. Contains 370433 sequences. (Running on oeis4.)