divides 
for all integers 
iff 
is squarefree and 
for all prime divisors 
of 
. Carmichael numbers satisfy
this criterion.
Korselt's Criterion
See also
Carmichael NumberExplore with Wolfram|Alpha
References
Borwein, D.; Borwein, J. M.; Borwein, P. B.; and Girgensohn, R. "Giuga's Conjecture on Primality." Amer. Math. Monthly 103, 40-50, 1996.Referenced on Wolfram|Alpha
Korselt's CriterionCite this as:
Weisstein, Eric W. "Korselt's Criterion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KorseltsCriterion.html