On the total number of prime factors   of an odd perfect number

Iannucci, Douglas E.; Sorli, Ronald M.

doi:10.1090/s0025-5718-03-01522-9

Cited by 11 publications

(6 citation statements)

References 16 publications

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“…Sayers showed that Ω(N ) ≥ 29 [11]. This was later extended by Iannucci and Sorli to show that Ω(N ) ≥ 37 [7]. This paper extends these results to give Theorem 1.1.…”

Section: Introductionmentioning

confidence: 54%

“…We keep descending in this manner until such time as we derive a contradiction. As in [7], we consider the primes in the order from smallest to largest. As in [7], we only partially factor large numbers, unless it becomes necessary to completely factor them.…”

Section: Lemma 24 Using the Notation Of Definition 23mentioning

confidence: 99%

“…As in [7], we consider the primes in the order from smallest to largest. As in [7], we only partially factor large numbers, unless it becomes necessary to completely factor them. In the output these are denoted as "c n" where n is the number of digits of the unfactored number.…”

Section: Lemma 24 Using the Notation Of Definition 23mentioning

confidence: 99%

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More on the total number of prime factors of an odd perfect number

Hare

2004

Math. Comp.

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“…Sayers showed that Ω(N ) ≥ 29 [11]. This was later extended by Iannucci and Sorli to show that Ω(N ) ≥ 37 [7]. This paper extends these results to give Theorem 1.1.…”

Section: Introductionmentioning

confidence: 54%

Section: Lemma 24 Using the Notation Of Definition 23mentioning

confidence: 99%

See 1 more Smart Citation

More on the total number of prime factors of an odd perfect number

Hare

2004

Math. Comp.

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“…For example, McDaniel proved in [7] that N is not perfect if each β i ≡ 1 (mod 3). Iannucci and Sorli, in [5], showed N is not perfect if 3|N and each β i ≡ 1 (mod 3) or β i ≡ 2 (mod 5). See Evans and Pearlman, [3] for a more detailed account of these types of results.…”

Section: Introductionmentioning

confidence: 99%

More on the Nonexistence of Odd Perfect Numbers of a Certain Form

Brown¹

2015

Preprint

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Euler showed that if an odd perfect number exists, it must be of the form N = p α q 2β 1 1 . . . q 2β k k , where p, q 1 , . . . , q k are distinct odd primes, α, β 1 , . . . , β k ∈ N, with p ≡ α ≡ 1 (mod 4). In 2005, Evans and Pearlman showed that N is not perfect, if 3|N or 7|N and each β i ≡ 2 (mod 5). We improve on this result by removing the hypothesis that 3|N or 7|N and show that N is not perfect, simply, if each β i ≡ 2 (mod 5).

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“…Sayers showed that Ω(N ) ≥ 29 [12]. Iannucci and Sorli showed that Ω(N ) ≥ 37 [8]. The author extended this to give Ω(N ) ≥ 47 [7].…”

Section: Introductionmentioning

confidence: 99%