A CLASS OF NEW NEAR-PERFECT NUMBERS

Title & Authors
A CLASS OF NEW NEAR-PERFECT NUMBERS
LI, YANBIN; LIAO, QUNYING;

Abstract
Let $\small{{\alpha}}$ be a positive integer, and let $\small{p_1}$, $\small{p_2}$ be two distinct prime numbers with $\small{p_1}$ < $\small{p_2}$. By using elementary methods, we give two equivalent conditions of all even near-perfect numbers in the form $\small{2^{\alpha}p_1p_2}$ and $\small{2^{\alpha}p_1^2p_2}$, 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 $\small{p_1=2^{{\alpha}+1}-1}$ and $\small{p_2={\frac{p^2_1+p_1+1}{3}}}$, where the former is a Mersenne prime and the latter's behavior is very much like a Fermat number.
Keywords
perfect number;pseudoperfect number;near-perfect number;k-near-perfect number;
Language
English
Cited by
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