A number which does not have any Friends. Solitary numbers include all Primes and Powers of Primes. More generally, numbers for which are solitary, where is the Greatest Common Divisor of and and is the Divisor Function. The first few solitary numbers are 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, ... (Sloane's A014567).

**References**

Anderson, C. W. and Hickerson, D. Problem 6020. ``Friendly Integers.'' *Amer. Math. Monthly* **84**,
65-66, 1977.

Sloane, N. J. A. Sequence A014567 in ``The On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.

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1999-05-26