Saralee Aursukaree, Prapanpong Pongsriiam
Published 2020-01-20Version 1
Let $n$ and $k$ be positive integers and $\sigma(n)$ the sum of all positive divisors of $n$. We call $n$ an exactly $k$-deficient-perfect number with deficient divisors $d_1, d_2, \ldots, d_k$ if $d_1, d_2, \ldots, d_k$ are distinct proper divisors of $n$ and $\sigma (n)=2n-(d_1+d_2+\ldots + d_k)$. In this article, we show that the only odd exactly $3$-deficient-perfect number with at most two distinct prime factors is $1521=3^2 \cdot 13^2$.
Primitive weird numbers having more than three distinct prime factors
On the Products $(1^\ell+1)(2^\ell+1)\cdots (n^\ell +1)$, II
On Deficient Perfect Numbers with Four Distinct Prime Factors
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