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 A164511 Least prime p such that p^2+1 is the product of n distinct primes. 0
 2, 3, 13, 47, 463, 2917, 30103, 241727, 3202337, 26066087, 455081827, 7349346113, 122872146223 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For n>1, there appear to be an infinite number of primes q for which q^2+1 is the product of n distinct primes (and thus has 2^n divisors). This sequence gives the smallest such prime for each n. See A048161 for primes q such that q^2+1 has two prime factors. Note that all prime factors of p^2+1 must be 2 or primes of the form 4k+1. LINKS EXAMPLE 1+2^2 = 5 1+3^2 = 2*5 1+13^2 = 2*5*17 1+47^2 = 2*5*13*17 1+463^2 = 2*5*13*17*97 1+2917^2 = 2*5*13*29*37*61 1+30103^2 = 2*5*13*17*41*73*137 1+241727^2 = 2*5*13*17*29*37*41*601 1+3202337^2 = 2*5*13*17*29*41*73*193*277 1+26066087^2 = 2*5*13*17*29*37*41*89*233*337 1+455081827^2 = 2*5*13*17*37*53*61*73*97*317*349 MATHEMATICA nn=8; t=Table[0, {nn}]; p=1; While[Times@@t==0, While[p=NextPrime[p]; {q, e}=Transpose[FactorInteger[p^2+1]]; !(Union[e]=={1} && Length[e]<=nn && t[[Length[e]]]==0)]; t[[Length[e]]]=p]; t CROSSREFS Sequence in context: A275556 A214888 A203985 * A184256 A105050 A184179 Adjacent sequences:  A164508 A164509 A164510 * A164512 A164513 A164514 KEYWORD hard,nonn AUTHOR T. D. Noe, Aug 14 2009 EXTENSIONS a(12)-a(13) from Donovan Johnson, Oct 09 2009 STATUS approved

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Last modified January 20 21:36 EST 2019. Contains 319336 sequences. (Running on oeis4.)