practical numbers

[franktaw at netscape.net]

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


-----Original Message-----
From: tanyakh at TanyaKhovanova.com

Hello seqfans,

There is some confusion with practical numbers. Wikipedia article on 
practical
numbers: http://en.wikipedia.org/wiki/Practical_number
gives the following definition of a practical number:
A practical number or panarithmic number is a positive integer n such 
that all
preceding positive integers are a sum of distinct divisors of n.

At the same time it refers to the sequence A005153 which gives a 
slightly
different definition:
Practical numbers (first definition): all k <= sigma(n) are sums of 
distinct
divisors of n. Also called panarithmic numbers.

Browsing other websites (including my own :-) ) I've found that the 
wiki
definition is used more often. Moreover, my calculation with the my 
definition
exactly matches the sequence A005153, though they are supposed to be 
different.

Please, clarify my confusion.

Tanya Khovanova


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