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 A105282 Positive integers n such that n^20 + 1 is semiprime (A001358). 11
 2, 4, 46, 154, 266, 472, 748, 1434, 1738, 2058, 2204, 2222, 2428, 2478, 2510, 2866, 3132, 3288, 3576, 3688, 3756, 4142, 4506, 4940, 5164, 6252, 6330, 6786, 7180, 7300, 7338, 7416, 7628, 7806, 9270, 9312, 10044, 10722, 10860, 12126, 12422, 12668, 12998, 13350 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS We have the polynomial factorization: n^20 + 1 = (n^4 + 1) * (n^16 - n^12 + n^8 - n^4 + 1). Hence after the initial n=1 prime, the binomial can never be prime. It can be semiprime iff n^4+1 is prime and (n^16 - n^12 + n^8 - n^4 + 1) is prime. LINKS Robert Price, Table of n, a(n) for n = 1..1405 FORMULA a(n)^20 + 1 is semiprime (A001358). EXAMPLE 2^20 + 1 = 1048577 = 17 * 61681, 4^20 + 1 = 1099511627777 = 257 * 4278255361, 46^20 + 1 = 1799519816997495209117766334283777 = 4477457 * 401906666439788301510827761, 1434^20 + 1 = 1352019721694375552250489804528860551814233886722212960509362177 = 4228599998737 * 319732233386510278346888399489424537759394853595121. MATHEMATICA Select[Range[1000000], PrimeQ[#^4 + 1] && PrimeQ[(#^20 + 1)/(#^4 + 1)] &] (* Robert Price, Mar 09 2015 *) PROG (MAGMA)IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [n: n in [1..1000] | IsSemiprime(n^20+1)] // Vincenzo Librandi, Dec 21 2010 CROSSREFS Cf. A000040, A001358, A006313, A103854, A104238, A104335, A105041, A105066, A105078, A105122, A105142, A105237, A104479, A104494, A104657. Sequence in context: A007596 A050588 A217795 * A018325 A099804 A019596 Adjacent sequences:  A105279 A105280 A105281 * A105283 A105284 A105285 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Apr 25 2005 EXTENSIONS a(9)-a(44) from Robert Price, Mar 09 2015 STATUS approved

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Last modified April 10 09:20 EDT 2021. Contains 342845 sequences. (Running on oeis4.)