Sketch of a proof that an odd perfect number relatively prime to $3$ has at least eleven prime factors
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- by Peter Hagis PDF
- Math. Comp. 40 (1983), 399-404 Request permission
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.References
- 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, DOI 10.1090/S0025-5718-1980-0572873-9
- 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 P. Hagis, Jr., "Every odd perfect number not divisible by 3 has at least eleven distinct prime factors." (Copy deposited in UMT file.)
- 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 371804, DOI 10.1090/S0025-5718-1975-0371804-2
- R. P. Jerrard and Nicholas Temperley, Almost perfect numbers, Math. Mag. 46 (1973), 84–87. MR 376511, DOI 10.2307/2689036
- 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 429716, DOI 10.1090/S0025-5718-1977-0429716-3
- Wayne L. McDaniel, On multiple prime divisors of cyclotomic polynomials, Math. Comput. 28 (1974), 847–850. MR 0387177, DOI 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), 265–300. MR 340169, DOI 10.4064/aa-25-3-265-300
Additional Information
- © Copyright 1983 American Mathematical Society
- 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