A CLASS OF NEW NEAR-PERFECT NUMBERS
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Let α be a positive integer, and let p1, p2 be two distinct prime numbers with p1 < p2. By using elementary methods, we give two equivalent conditions of all even near-perfect numbers in the form 2αp21p2 and 2αp21p2, and obtain a lot of new near-perfect numbers which involve some special kinds of prime number pairs. One kind is exactly the new Mersenne conjecture’s prime number pair. Another kind has the form p1=2α+1-1 and p2=p21+p1+1/3, where the former is a Mersenne prime and the latter’s behavior is very much like a Fermat number.
Abstract
Let α be a positive integer, and let p1, p2 be two distinct prime numbers with p1 < p2. By using elementary methods, we give two equivalent conditions of all even near-perfect numbers in the form 2αp21p2 and 2αp21p2, and obtain a lot of new near-perfect numbers which involve some special kinds of prime number pairs. One kind is exactly the new Mersenne conjecture’s prime number pair. Another kind has the form p1=2α+1-1 and p2=p21+p1+1/3, where the former is a Mersenne prime and the latter’s behavior is very much like a Fermat number.
참고문헌 (13)
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