Odd perfect numbers not divisible by 3. II

Kishore, Masao

doi:10.1090/S0025-5718-1983-0679456-3

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: 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 371804, 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 429716, 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 485658, https://doi.org/10.1090/S0025-5718-1978-0485658-X
[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 340169, https://doi.org/10.4064/aa-25-3-265-300
[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