The sequence defined by and the Recurrence Relation

(1) |

(2) |

(3) |

(4) |

(5) |

The of the first few Prime are 0, 1, 2, 3, 5, .... Vardi (1991) gives a lists of factors less than of for and shows that is Composite for . Furthermore, all numbers less than in Sylvester's sequence are Squarefree, and no Squareful numbers in this sequence are known (Vardi 1991).

**References**

Graham, R. L.; Knuth, D. E.; and Patashnik, O. Research problem 4.65 in
*Concrete Mathematics: A Foundation for Computer Science, 2nd ed.* Reading, MA: Addison-Wesley, 1994.

Sloane, N. J. A. Sequence
A000058/M0865
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
*The Encyclopedia of Integer Sequences.* San Diego: Academic Press, 1995.

Vardi, I. ``Are All Euclid Numbers Squarefree?'' and ```PowerMod` to the Rescue.'' §5.1 and 5.2 in
*Computational Recreations in Mathematica.* Reading, MA: Addison-Wesley, pp. 82-89, 1991.

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1999-05-26