Harmonic number (disambiguation)
From Wikipedia, the free encyclopedia
The term harmonic number has several different meanings:
- In number theory, the harmonic numbers are the sums of the inverses of integers, forming the harmonic series.
- In engineering, the phrase 'harmonic number' is sometimes loosely used to refer to the nth harmonic of a periodic wave.
- Philippe de Vitry, a 14th century French musicologist, defined a harmonic number as an integer that is not divisible by any prime other than 2 or 3. In 1342, the rabbi Gersonides, a contemporary of de Vitry, showed that there are only four pairs of such numbers that differ by one. The abc conjecture concerns a generalization of Gersonides results.
- Ivars Peterson's MathTrek: Medieval Harmony
- Harmonic divisor numbers, also called Ore numbers or Ore's harmonic numbers, are positive integers whose divisors have a harmonic mean that is an integer.
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