Sketch of a proof that an odd perfect number relatively prime to has at least eleven prime factors

Author:
Peter Hagis

Journal:
Math. Comp. **40** (1983), 399-404

MSC:
Primary 11A25; Secondary 11-04

DOI:
https://doi.org/10.1090/S0025-5718-1983-0679455-1

MathSciNet review:
679455

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Abstract: An argument is outlined which demonstates that every odd perfect number which is not divisible by 3 has at least eleven distinct prime factors.

**[1]**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**[2]**Peter Hagis Jr.,*On the second largest prime divisor of an odd perfect number*, Analytic number theory (Philadelphia, Pa., 1980) Lecture Notes in Math., vol. 899, Springer, Berlin-New York, 1981, pp. 254–263. MR**654532****[3]**P. Hagis, Jr., "Every odd perfect number not divisible by 3 has at least eleven distinct prime factors." (Copy deposited in UMT file.)**[4]**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**[5]**R. P. Jerrard and Nicholas Temperley,*Almost perfect numbers*, Math. Mag.**46**(1973), 84–87. MR**0376511**, https://doi.org/10.2307/2689036**[6]**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**[7]**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**[8]**Carl Pomerance,*Odd perfect numbers are divisible by at least seven distinct primes*, Acta Arith.**25**(1973/74), 265–300. MR**0340169**, https://doi.org/10.4064/aa-25-3-265-300

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DOI:
https://doi.org/10.1090/S0025-5718-1983-0679455-1

Article copyright:
© Copyright 1983
American Mathematical Society