Giuga number

A Giuga number is a squarefree composite number $n$ such that each prime factor $p_i|(\frac{n}{p_i}-1)$. For these numbers it then follows that $n{B}_{\varphi (n)}\equiv -1modn$, (where $B_x$ is a Bernoulli number).

The first few Giuga numbers are 30, 858, 1722, 66198, 2214408306, 24423128562 (listed in sequence A007850 of Sloane’s OEIS).

All known Giuga numbers are even and have at least three factors. An odd Giuga number would have to have at least twelve factors.

Title	Giuga number
Canonical name	GiugaNumber
Date of creation	2013-03-22 15:50:22
Last modified on	2013-03-22 15:50:22
Owner	Mravinci (12996)
Last modified by	Mravinci (12996)
Numerical id	7
Author	Mravinci (12996)
Entry type	Definition
Classification	msc 11D85
Related topic	PrimaryPseudoperfectNumber