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harmonic divisor numbers
A number is called harmonic divisor number if the harmonic mean of its divisors is an integer. This is equivalent to say that the average of the divisors of divides , i.e., is an integer.

Harmonic divisor numbers are also called harmonic numbers, for brevity, or Ore numbers, after O.Ore who studied them.

O.Ore proved that all the perfect numbers are also harmonic and conjectured that 1 is the only odd harmonic number. This conjecture has been verified by G.L.Cohen et al. for and if true, it will imply that no odd perfect numbers exist.

Jaycob Coleman has observed that all the Ore numbers up to are also practical numbers and conjectured this holds in general.

T. Goto and K. Okeya have computed a list of the 937 harmonic numbers up to .

The first harmonic numbers are 1, 6, 28, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190, 18600, 18620, 27846, 30240, 32760, 55860, 105664, 117800, 167400, 173600, 237510 more terms

Harmonic numbers can also be... (you may click on names or numbers and on + to get more values)