Ore,s Conjecture
المؤلف:
Sloane, N. J. A
المصدر:
Sequences A099377 and A099378 in
الجزء والصفحة:
...
26-11-2020
1059
Ore,s Conjecture
Define the harmonic mean of the divisors of 
where 
is the divisor function (the number of divisors of 
).
For 
, 2, ..., the values of 
are then 1, 4/3, 3/2, 12/7, 5/3, 2, 7/4, 32/15, 27/13, 20/9, ... (OEIS A099377 and A099378).
If 
is a perfect number, 
is an integer.
Ore conjectured that if 
is odd, then 
is not an integer. This implies that no odd perfect numbers exist.
REFERENCES:
Sloane, N. J. A. Sequences A099377 and A099378 in "The On-Line Encyclopedia of Integer Sequences."
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