| 1. | The difference between any two harmonic numbers is never an integer.
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| 2. | No harmonic numbers are integers, except for 1 } }.
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| 3. | Where H _ n is the n-th harmonic number.
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| 4. | There are several infinite summations involving harmonic numbers and powers of ?:
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| 5. | Which may be thought of as a generalization of a harmonic number.
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| 6. | The 227th harmonic number is the first to exceed six.
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| 7. | The problem was to characterize all pairs of harmonic numbers differing by 1.
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| 8. | Where is the th harmonic number, and is the Euler Mascheroni constant.
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| 9. | Double the harmonic number means double the frequency ( which sounds an octave higher ).
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| 10. | Harmonic numbers were studied in antiquity and are important in various branches of number theory.
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