Odd perfect numbers not divisible by $3$. II
Author:
Masao Kishore
Journal:
Math. Comp. 40 (1983), 405-411
MSC:
Primary 10A20
DOI:
https://doi.org/10.1090/S0025-5718-1983-0679456-3
MathSciNet review:
679456
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We prove that odd perfect numbers not divisible by 3 have at least eleven distinct prime factors.
-
J. E. Z. Chein, An Odd Perfect Number Has at Least 8 Prime Factors, Ph.D. Thesis, Pennsylvania State University, 1979.
- Peter Hagis Jr., Outline of a proof that every odd perfect number has at least eight prime factors, Math. Comp. 35 (1980), no. 151, 1027โ1032. MR 572873, DOI https://doi.org/10.1090/S0025-5718-1980-0572873-9
- Peter Hagis Jr. and Wayne L. McDaniel, On the largest prime divisor of an odd perfect number. II, Math. Comp. 29 (1975), 922โ924. MR 371804, DOI https://doi.org/10.1090/S0025-5718-1975-0371804-2
- Masao Kishore, Odd perfect numbers not divisible by $3$ are divisible by at least ten distinct primes, Math. Comp. 31 (1977), no. 137, 274โ279. MR 429716, DOI https://doi.org/10.1090/S0025-5718-1977-0429716-3
- Masao Kishore, Odd integers $N$ with five distinct prime factors for which $2-10^{-12}<\sigma (N)/N<2+10^{-12}$, Math. Comp. 32 (1978), no. 141, 303โ309. MR 485658, DOI https://doi.org/10.1090/S0025-5718-1978-0485658-X
- Wayne L. McDaniel, On multiple prime divisors of cyclotomic polynomials, Math. Comput. 28 (1974), 847โ850. MR 0387177, DOI https://doi.org/10.1090/S0025-5718-1974-0387177-4
- Carl Pomerance, Odd perfect numbers are divisible by at least seven distinct primes, Acta Arith. 25 (1973/74), 265โ300. MR 340169, DOI https://doi.org/10.4064/aa-25-3-265-300
- Carl Pomerance, The second largest prime factor of an odd perfect number, Math. Comput. 29 (1975), 914โ921. MR 0371801, DOI https://doi.org/10.1090/S0025-5718-1975-0371801-7
Retrieve articles in Mathematics of Computation with MSC: 10A20
Retrieve articles in all journals with MSC: 10A20
Additional Information
Article copyright:
© Copyright 1983
American Mathematical Society