Giuga number

A Giuga number is a squarefree composite number $n$ such that each prime factor $p_{i}|({n\over{p_{i}}}-1)$. For these numbers it then follows that $nB_{\phi(n)}\equiv-1\bmod n$, (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 GiugaNumber 2013-03-22 15:50:22 2013-03-22 15:50:22 Mravinci (12996) Mravinci (12996) 7 Mravinci (12996) Definition msc 11D85 PrimaryPseudoperfectNumber