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Practical numbers

Definition

In the set N of positive integers :
n is practical if any k, 1 leq k leq n, is the sum of one or several distinct dividers of n

Property (Stewart) :
If the pi> 1 are the prime factors of n, arranging in the order ascending, n is practical if and only if
a) p1=2 and if
b) for i=2,3, ..., k,   pi is lower or equal to 1 + the sum of the dividers using only the prime factors lower strictly thanpi.
This number is it practical?  

Liens

Practical numbers
prnstewart.c   C Program of calculation of the table of the practical numbers (licence GPL)
Table of practical numbers up to 100 000
Practical Number MathWorld A number n is practical if for all k < n, k is the sum of distinct proper divisors of n.
Rapport de la 34ième Olympiade mathématique du Canada
A survey on practical numbers Définitions équivalentes, propriétés - Giuseppe Melfi
Practical numbers Giuseppe Melfi
Some Problems in Elementary Number Theory and Modular forms (PDF) Giuseppe Melfi 1998
Egyptian Fractions Kevin Gong 1992 (U.C. Berkeley Professor Andrew Ogg
A005153 Practical numbers (first definition): all k <= sigma(n) are sums of distinct divisors of n. Also called panarithmic numbers.