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Untouchable Number

An untouchable number is an Integer which is not the sum of the Proper Divisors of any other number. The first few are 2, 5, 52, 88, 96, 120, 124, 146, ... (Sloane's A005114). Erdös has proven that there are infinitely many. It is thought that 5 is the only Odd untouchable number.


Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 840, 1972.

Guy, R. K. ``Untouchable Numbers.'' §B10 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 66-67, 1994.

Sloane, N. J. A. Sequence A005114/M1552 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein