practical numbers

[Tanya Khovanova]

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