On weird and pseudoperfect numbers
Authors:
S. J. Benkoski and P. Erdős
Journal:
Math. Comp. 28 (1974), 617623
MSC:
Primary 10A40
Corrigendum:
Math. Comp. 29 (1975), 673674.
Corrigendum:
Math. Comp. 29 (1975), 673.
MathSciNet review:
0347726
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Abstract: If n is a positive integer and denotes the sum of the divisors of n, then n is perfect if , abundant if and deficient if . n is called pseudoperfect if n is the sum of distinct proper divisors of n. If n is abundant but not pseudoperfect, then n is called weird. The smallest weird number is 70. We prove that the density of weird numbers is positive and discuss several related problems and results. A list of all weird numbers not exceeding is given.
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 Y. Motohashi, "A note on the least prime in an arithmetic progression with a prime difference," Acta Arith., v. 17, 1970, pp. 283285. MR 42 #3030. MR 0268131 (42:3030)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197403477269
PII:
S 00255718(1974)03477269
Keywords:
Weird numbers,
pseudoperfect numbers,
primitive abundant numbers
Article copyright:
© Copyright 1974
American Mathematical Society
