Harmonic divisor number

This article is about harmonic divisor numbers. For meanings of harmonic number, see harmonic number (disambiguation).

In mathematics, a harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are

1, 6, 28, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190 (sequence A001599 in the OEIS).

Harmonic divisor numbers were introduced by Øystein Ore, who showed that every perfect number is a harmonic divisor number and conjectured that there are no odd harmonic divisor numbers other than 1.