Usually means: Sum of reciprocals of integers.
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We found 5 dictionaries that define the word harmonic number:

General (2 matching dictionaries)
  1. harmonic number: Wiktionary
  2. Harmonic number (disambiguation), Harmonic number: Wikipedia, the Free Encyclopedia

Science (3 matching dictionaries)
  1. Harmonic Number: Eric Weisstein's World of Mathematics
  2. Harmonic Number: Eric Weisstein's World of Physics
  3. harmonic number: PlanetMath Encyclopedia

Definitions from Wiktionary (harmonic number)

noun:  (number theory) Any of a series of numbers formed from the sum of the reciprocals of consecutive natural numbers

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