Let $\sigma(n)$ be the sum of the positive divisors of $n$. A number $n$ is non-deficient if $\sigma(n) \geq 2n$. We establish new lower bounds for the number of distinct prime factors of an odd non-deficient number in terms of its second smallest, third smallest and fourth smallest prime factors. Tighter bounds are obtained for odd perfect numbers. We also discuss the behavior of $\sigma(n!+1)$, $\sigma(2^n+1)$, and related sequences
In this work we construct a lower bound for an odd perfect number in terms of the number of its dist...
Recently, Pollack and Shevelev introduced the concept of near-perfect numbers in Journal of Number ...
Recently, Pollack and Shevelev introduced the concept of near-perfect numbers in Journal of Number ...
Let $\sigma(n)$ to be the sum of the positive divisors of $n$. A number is non-deficient if $\sigma(...
For a positive integer $n$, let $\sigma(n)$ denote the sum of the positive divisors of $n$, and le...
For a positive integer \(n\), let \(\sigma(n)\) denote the sum of the positive divisors of \(n\). Le...
If N is an odd perfect number with k distinct prime factors then we show that N < 2^(4k) . If some o...
Abstract. Let σ(n) denote the sum of the positive divisors of n. We say that n is perfect if σ(n) =...
Suppose \(N\) be a positive odd number with \(r\) distinct prime factors and \(N\) divides \(\sigm...
AbstractWe investigate lower bounds for ω((sn)) − ω((rn)) that are independent of n. This difference...
Suppose \(N\) be a positive odd number with \(r\) distinct prime factors and \(N\) divides \(\sigm...
We say n ∈ ℕ is perfect if σ (n) = 2n, where σ(n) denotes the sum of the positive divisors of n. No ...
In this work we construct a lower bound for an odd perfect number in terms of the number of its dist...
Recently, Pollack and Shevelev introduced the concept of near-perfect numbers in Journal of Number ...
Recently, Pollack and Shevelev introduced the concept of near-perfect numbers in Journal of Number ...
In this work we construct a lower bound for an odd perfect number in terms of the number of its dist...
Recently, Pollack and Shevelev introduced the concept of near-perfect numbers in Journal of Number ...
Recently, Pollack and Shevelev introduced the concept of near-perfect numbers in Journal of Number ...
Let $\sigma(n)$ to be the sum of the positive divisors of $n$. A number is non-deficient if $\sigma(...
For a positive integer $n$, let $\sigma(n)$ denote the sum of the positive divisors of $n$, and le...
For a positive integer \(n\), let \(\sigma(n)\) denote the sum of the positive divisors of \(n\). Le...
If N is an odd perfect number with k distinct prime factors then we show that N < 2^(4k) . If some o...
Abstract. Let σ(n) denote the sum of the positive divisors of n. We say that n is perfect if σ(n) =...
Suppose \(N\) be a positive odd number with \(r\) distinct prime factors and \(N\) divides \(\sigm...
AbstractWe investigate lower bounds for ω((sn)) − ω((rn)) that are independent of n. This difference...
Suppose \(N\) be a positive odd number with \(r\) distinct prime factors and \(N\) divides \(\sigm...
We say n ∈ ℕ is perfect if σ (n) = 2n, where σ(n) denotes the sum of the positive divisors of n. No ...
In this work we construct a lower bound for an odd perfect number in terms of the number of its dist...
Recently, Pollack and Shevelev introduced the concept of near-perfect numbers in Journal of Number ...
Recently, Pollack and Shevelev introduced the concept of near-perfect numbers in Journal of Number ...
In this work we construct a lower bound for an odd perfect number in terms of the number of its dist...
Recently, Pollack and Shevelev introduced the concept of near-perfect numbers in Journal of Number ...
Recently, Pollack and Shevelev introduced the concept of near-perfect numbers in Journal of Number ...
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