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).
See also Friend
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.