Abstract

In an earlier Report (NM-R9212, June 1992), two of us gave tables of factorizations of a n \Sigma 1 for 13 a ! 100. The exponents n satisfied a n ! 10 255 if a ! 30, and n 100 if a 30. The factorizations were complete for n 46, and the tables contained no composite numbers smaller than 10 80 . In this Report we update the original tables. The factorizations are now complete for n 58, and there are no composite numbers smaller than 10 86 . 1991 Mathematics Subject Classification: Primary 11A25; Secondary 11-04. Keywords and Phrases: Factor Tables. 1. Introduction For many years there has been an interest in the prime factors of numbers of the form a n \Sigma 1, where a is a small integer (the base) and n is a positive exponent. Such numbers often arise. For example, if a is prime then there is a finite field F with a n elements, and the multiplicative group of F has a n \Gamma 1 elements. Also, for prime a the sum of divisors of a n is oe(a n ) = (a n+1 ...

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