Primitive -abundant numbers

Author:
Graeme L. Cohen

Journal:
Math. Comp. **43** (1984), 263-270

MSC:
Primary 11A25

MathSciNet review:
744936

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Abstract: A number *N* is primitive -abundant if for all proper divisors *M* of *N*. In this paper, we tabulate, for , all such *N* for which is greatest. We show that, if *N* is primitive -abundant and , then .

**[1]**Graeme L. Cohen,*On primitive abundant numbers*, J. Austral. Math. Soc. Ser. A**34**(1983), no. 1, 123–137. MR**683184****[2]**P. Erdős,*Remarks on number theory. I. On primitive 𝛼-abundant numbers*, Acta Arith.**5**(1958), 25–33 (1959). MR**0101211****[3]**Harold N. Shapiro,*Note on a theorem of Dickson*, Bull. Amer. Math. Soc.**55**(1949), 450–452. MR**0028886**, 10.1090/S0002-9904-1949-09238-8**[4]**Harold N. Shapiro,*On primitive abundant numbers*, Comm. Pure Appl. Math.**21**(1968), 111–118. MR**0218298**

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DOI:
https://doi.org/10.1090/S0025-5718-1984-0744936-X

Article copyright:
© Copyright 1984
American Mathematical Society