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Superharmonic numbers
Author(s):
Graeme
L.
Cohen.
Journal:
Math. Comp.
78
(2009),
421-429.
MSC (2000):
Primary 11A25, 11Y70
Posted:
September 5, 2008
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Abstract:
Let  denote the number of positive divisors of a natural number  and let  denote their sum. Then  is superharmonic if  for some positive integer  . We deduce numerous properties of superharmonic numbers and show in particular that the set of all superharmonic numbers is the first nontrivial example that has been given of an infinite set that contains all perfect numbers but for which it is difficult to determine whether there is an odd member.
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Additional Information:
Graeme
L.
Cohen
Affiliation:
Department of Mathematical Sciences, University of Technology, Sydney, Broadway, NSW 2007, Australia
Address at time of publication:
1201/95 Brompton Road, Kensington, NSW 2033, Australia
Email:
g.cohen@bigpond.net.au
DOI:
10.1090/S0025-5718-08-02147-9
PII:
S 0025-5718(08)02147-9
Received by editor(s):
April 12, 2007
Received by editor(s) in revised form:
January 22, 2008
Posted:
September 5, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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