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]**P. Hagis, Jr., "Outline of a proof that every odd perfect number has at least eight prime factors,"*Math. Comp.*, v. 35, 1980, pp. 1027-1032. MR**572873 (81k:10004)****[2]**P. Hagis, Jr., "On the second largest prime divisor of an odd perfect number,"*Analytic Number Theory*, Lecture Notes in Math., vol. 899, Springer-Verlag, Berlin and New York, 1981, pp. 254-263. MR**654532 (83i:10004)****[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]**P. Hagis, Jr. & W. L. McDaniel, "On the largest prime divisor of an odd perfect number. II,"*Math. Comp.*, v. 29, 1975, pp. 922-924. MR**0371804 (51:8021)****[5]**R. P. Jerrard & N. Temperley, "Almost perfect numbers,"*Math. Mag.*, v. 46, 1973, pp. 84-87. MR**0376511 (51:12686)****[6]**M. Kishore, "Odd perfect numbers not divisible by 3 are divisible by at least ten distinct primes,"*Math. Comp.*, v. 31, 1977, pp. 274-279. MR**0429716 (55:2727)****[7]**W. L. McDaniel, "On multiple prime divisors of cyclotomic polynomials,"*Math. Comp.*, v. 28, 1974, pp. 847-850. MR**0387177 (52:8022)****[8]**C. Pomerance, "Odd perfect numbers are divisible by at least seven distinct primes,"*Acta Arith.*, v. 25, 1974, pp. 265-300. MR**0340169 (49:4925)**

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

Article copyright:
© Copyright 1983
American Mathematical Society