Odd perfect numbers not divisible by . 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

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that odd perfect numbers not divisible by 3 have at least eleven distinct prime factors.

**[1]**J. E. Z. Chein,*An Odd Perfect Number Has at Least 8 Prime Factors*, Ph.D. Thesis, Pennsylvania State University, 1979.**[2]**Peter Hagis Jr.,*Outline of a proof that every odd perfect number has at least eight prime factors*, Math. Comp.**35**(1980), no. 151, 1027–1032. MR**572873**, https://doi.org/10.1090/S0025-5718-1980-0572873-9**[3]**Peter Hagis Jr. and Wayne L. McDaniel,*On the largest prime divisor of an odd perfect number. II*, Math. Comp.**29**(1975), 922–924. MR**0371804**, https://doi.org/10.1090/S0025-5718-1975-0371804-2**[4]**Masao Kishore,*Odd perfect numbers not divisible by 3 are divisible by at least ten distinct primes*, Math. Comp.**31**(1977), no. 137, 274–279. MR**0429716**, https://doi.org/10.1090/S0025-5718-1977-0429716-3**[5]**Masao Kishore,*Odd integers 𝑁 with five distinct prime factors for which 2-10⁻¹²<𝜎(𝑁)/𝑁<2+10⁻¹²*, Math. Comp.**32**(1978), no. 141, 303–309. MR**0485658**, https://doi.org/10.1090/S0025-5718-1978-0485658-X

Masao Kishore,*Addendum: “Odd integers 𝑁 with five distinct prime factors for which 2-10⁻¹²<𝜎(𝑁)/𝑁<2+10⁻¹²” (Math. Comp. 32 (1978), no. 141, 303–309)*, Math. Comp.**32**(1978), no. 141, loose microfiche suppl., 12. MR**0485659**, https://doi.org/10.2307/2006281**[6]**Wayne L. McDaniel,*On multiple prime divisors of cyclotomic polynomials*, Math. Comput.**28**(1974), 847–850. MR**0387177**, https://doi.org/10.1090/S0025-5718-1974-0387177-4**[7]**Carl Pomerance,*Odd perfect numbers are divisible by at least seven distinct primes*, Acta Arith.**25**(1973/74), 265–300. MR**0340169****[8]**Carl Pomerance,*The second largest prime factor of an odd perfect number*, Math. Comput.**29**(1975), 914–921. MR**0371801**, https://doi.org/10.1090/S0025-5718-1975-0371801-7

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1983-0679456-3

Article copyright:
© Copyright 1983
American Mathematical Society