
Glossary: Prime Pages: Top 5000: 
The hardware and software on this system was updated September 4th.
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<caldwell@utm.edu> Recall that a perfect number is an integer that is the sum of its aliquot divisors, that is, all of its positive divisors except itself. Another way to say this is: n is perfect if the sum of all of its positive divisors, denoted sigma(n), is twice n. Any positive integer n which divides the sum of its positive divisors is called multiply perfect or kperfect where k is the index sigma(n)/n. For example, here are the smallest multiply perfect numbers for their index:
Fermat (not Carmichael) was the first to find a 6perfect number (in 1643): 34111227434420791224041472000.You might want to try your hand at proving the following theorems:
See Also: SigmaFunction, PerfectNumber Related pages (outside of this work)
Chris K. Caldwell © 19992014 (all rights reserved)
