Abstract:
For a positive integer n, let σ(n) denote the sum of the positive divisors of n. Let d be a proper divisor of n, we call n a deficient-perfect number if
σ(n)=2n-d . On the basis of the references, we characterize some properties of odd deficient-perfect numbers with four distinct prime divisors. We prove that if
is an odd deficient-perfect number, then p
1 = 3, p
2 ≤ 13, and improve the result of the references.