practical numbers

[David Wilson]

Assuming Franklin's observation to be correct, why not

%C A005153 Also, n such that all k <= n are sums of distinct divisors of n.

Some poorly-thought-out questions before I head off to work:

Are there not-quite-practical numbers, that is, numbers such that n-1 is the 
only number < n which is not the sum of distinct divisors of n?

If not, is there some interesting bound f(n) < n such that if all k <= f(n) 
are sums of distinct divisors of n, then n is also a sum of distinct 
divisors of n?

----- Original Message ----- 
From: <franktaw at netscape.net>
To: <tanyakh at TanyaKhovanova.com>; <seqfan at ext.jussieu.fr>
Sent: Monday, November 27, 2006 12:04 PM
Subject: Re: practical numbers


> The definitions are equivalent.  The condition cited in the Wikipedia 
> article, to make everything up to n a sum of the divisors of n, is 
> sufficient to make everything up to sigma(n) be such a sum.
>
> Franklin T. Adams-Watters