From: Clive Tooth
Subject: Re: Untouchable numbers
Date: Wed, 20 Jan 1999 21:30:09 +0000
Newsgroups: sci.math
Keywords: (Numbers not the sum of divisors)
Margie Hilson wrote:
> On p.41 of David Wells' PENGUIN DICTIONARY OF CURIOUS AND INTERESTING
> NUMBERS (Revised Edition), he writes, "5 is probably the only odd
> untouchable number." Could someone give me a pointer to a definition of an
> "untouchable number" (without a reference about Chicago bootlegging during
> Prohibition :)? Thanks, Margie.
An untouchable number is a number which is not the sum of the proper
divisors of any number. A proper divisor of a number is any divisor of
the number, except itself. Thus the proper divisors of 12 are 1, 2, 3, 4
and 6. It is known that there are infinitely many untouchable numbers. 5
is the only known odd one. See sequence A005114 at
http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi
. "proper divisors" are sometimes called "aliquot parts", however
"aliquot parts" is sometimes defined to include the number itself.
--
Clive Tooth
http://www.pisquaredoversix.force9.co.uk/
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