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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

Table of n, a(n) for n=1..13.

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 February 21 19:26 EST 2018. Contains 299422 sequences. (Running on oeis4.)