Add to ORKGInternational audienceEllia recently proved that if N is an odd perfect number such that rad(N) > √N, then its special prime p satisfies p > 148207 if 3 # N and p > 223 otherwise. He also suggested that these bounds can be improved with some computation. We obtain that if N is an odd perfect number such that rad(N) > √N, then p > 10 60
As shown by Euler an odd perfect number n must be of the form n=p^α m^2 where p≡α≡1 (mod 4) and p is...
Abstract. Let σ(n) denote the sum of the positive divisors of n. We say that n is perfect if σ(n) =...
As shown by Euler an odd perfect number n must be of the form n=p^α m^2 where p≡α≡1 (mod 4) and p is...
International audienceEllia recently proved that if N is an odd perfect number such that rad(N) > √N...
International audienceBrent, Cohen, and te Riele proved in 1991 that an odd perfect number N is grea...
International audienceBrent, Cohen, and te Riele proved in 1991 that an odd perfect number N is grea...
Suppose \(N\) be a positive odd number with \(r\) distinct prime factors and \(N\) divides \(\sigm...
Suppose \(N\) be a positive odd number with \(r\) distinct prime factors and \(N\) divides \(\sigm...
Abstract. A 1913 theorem of Dickson asserts that for each fixed natural number k, there are only fin...
If N is an odd perfect number with k distinct prime factors then we show that N < 2^(4k) . If some o...
In this work we construct a lower bound for an odd perfect number in terms of the number of its dist...
We say n ∈ ℕ is perfect if σ (n) = 2n, where σ(n) denotes the sum of the positive divisors of n. No ...
Abstract. Let σ(n) denote the sum of positive divisors of the natural number n. Such a number is sai...
It has been known since the time of Euler that an odd perfect number N (if it exists) must have the ...
In this work we construct a lower bound for an odd perfect number in terms of the number of its dist...
As shown by Euler an odd perfect number n must be of the form n=p^α m^2 where p≡α≡1 (mod 4) and p is...
Abstract. Let σ(n) denote the sum of the positive divisors of n. We say that n is perfect if σ(n) =...
As shown by Euler an odd perfect number n must be of the form n=p^α m^2 where p≡α≡1 (mod 4) and p is...
International audienceEllia recently proved that if N is an odd perfect number such that rad(N) > √N...
International audienceBrent, Cohen, and te Riele proved in 1991 that an odd perfect number N is grea...
International audienceBrent, Cohen, and te Riele proved in 1991 that an odd perfect number N is grea...
Suppose \(N\) be a positive odd number with \(r\) distinct prime factors and \(N\) divides \(\sigm...
Suppose \(N\) be a positive odd number with \(r\) distinct prime factors and \(N\) divides \(\sigm...
Abstract. A 1913 theorem of Dickson asserts that for each fixed natural number k, there are only fin...
If N is an odd perfect number with k distinct prime factors then we show that N < 2^(4k) . If some o...
In this work we construct a lower bound for an odd perfect number in terms of the number of its dist...
We say n ∈ ℕ is perfect if σ (n) = 2n, where σ(n) denotes the sum of the positive divisors of n. No ...
Abstract. Let σ(n) denote the sum of positive divisors of the natural number n. Such a number is sai...
It has been known since the time of Euler that an odd perfect number N (if it exists) must have the ...
In this work we construct a lower bound for an odd perfect number in terms of the number of its dist...
As shown by Euler an odd perfect number n must be of the form n=p^α m^2 where p≡α≡1 (mod 4) and p is...
Abstract. Let σ(n) denote the sum of the positive divisors of n. We say that n is perfect if σ(n) =...
As shown by Euler an odd perfect number n must be of the form n=p^α m^2 where p≡α≡1 (mod 4) and p is...