A CLASS OF NEW NEAR-PERFECT NUMBERS LI, YANBIN; LIAO, QUNYING;
Let be a positive integer, and let , be two distinct prime numbers with < . By using elementary methods, we give two equivalent conditions of all even near-perfect numbers in the form and , 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 and , where the former is a Mersenne prime and the latter's behavior is very much like a Fermat number.