منابع مشابه
On Perfect and Near-perfect Numbers
We call n a near-perfect number if n is the sum of all of its proper divisors, except for one of them, which we term the redundant divisor. For example, the representation 12 = 1 + 2 + 3 + 6 shows that 12 is near-perfect with redundant divisor 4. Near-perfect numbers are thus a very special class of pseudoperfect numbers, as defined by Sierpiński. We discuss some rules for generating near-perfe...
متن کاملOn Perfect Totient Numbers
Let n > 2 be a positive integer and let φ denote Euler’s totient function. Define φ(n) = φ(n) and φ(n) = φ(φ(n)) for all integers k ≥ 2. Define the arithmetic function S by S(n) = φ(n) + φ(n) + · · ·+ φ(n) + 1, where φ(n) = 2. We say n is a perfect totient number if S(n) = n. We give a list of known perfect totient numbers, and we give sufficient conditions for the existence of further perfect ...
متن کاملOdd Perfect numbers
It is not known whether or not odd perfect numbers can exist. However it is known that there is no such number below 10, (see Brent [1]). Moreover it has been proved by Hagis [4] and Chein [2] independently that an odd perfect number must have at least 8 prime factors. In fact results of this latter type can in principle be obtained solely by calculation, in view of the result of Pomerance [6] ...
متن کاملPerfect Numbers in ACL2
A perfect number is a positive integer n such that n equals the sum of all positive integer divisors of n that are less than n. That is, although n is a divisor of n, n is excluded from this sum. Thus 6 = 1 + 2 + 3 is perfect, but 12 6= 1 + 2 + 3 + 4 + 6 is not perfect. An ACL2 theory of perfect numbers is developed and used to prove, in ACL2(r), this bit of mathematical folklore: Even if there...
متن کاملAbout k-perfect numbers
ABSTRACT. In this paper we present some results about k-perfect numbers, and generalize two inequalities due to M. Perisastri (see [6]).
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2012
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2012.06.008