Primitive $\alpha $-abundant numbers

On the distribution of primitive abundant numbers

On Totient Abundant Numbers

In this note, we find an asymptotic formula for the counting function of the set of totient abundant numbers.

Νοτε Ον Consecutive Abundant Numbers

A positive integer N is called an abundant number if σ(N) > 2N, where σ (N) denotes the suns of the divisors of N including 1 and N. Abundant numbers have been recently investigated by Behrend, Chowla, Davenport , myself, and others ; it has been proved, for example, that they have a density greater than 0 . I prove now the following THEOREM. We can find two constants c l , c 2 such that , for ...

Abundant Numbers and the Riemann Hypothesis

Least primitive root of prime numbers

Let p be a prime number. Fermat's little theorem [1] states that a^(p-1) mod p=1 (a hat (^) denotes exponentiation) for all integers a between 1 and p-1. A primitive root [1] of p is a number r such that any integer a between 1 and p-1 can be expressed by a=r^k mod p, with k a nonnegative integer smaller that p-1. If p is an odd prime number then r is a primitive root of p if and only if r^((p-...