Solitary Number

A number which does not have any Friends. Solitary numbers include all Primes and Powers of Primes. More generally, numbers for which $(n,\sigma(n))=1$ are solitary, where $(a,b)$ is the Greatest Common Divisor of $a$ and $b$ and $\sigma(n)$ 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.