![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() |
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.