A composite number
is called Giuga number
for all prime divisors
It can be proved that is a Giuga number if and only if the
ranges among the divisors of
, represents a natural number.
For example, is a Giuga number because
It can be proved easily that a Giuga number must be squarefree and equal to the product of at least 3 primes.
All the known Giuga numbers are even, but the possibility of an odd Giuga number has not been ruled out.
The first Giuga numbers are
30, 858, 1722, 66198, 2214408306, 24423128562, 432749205173838.
Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
A graph displaying how many Giuga numbers are multiples of the primes p
from 2 to 71. In black the ideal line 1/p