[seqfan] A253236

[Peter Lawrence]

A253236    "The unique prime p <= n such that n-th cyclotomic  
polynomial has a root mod p, or 0 if no such p exists."

0, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 0, 13, 7, 0, 2, 17, 3, 19, 5, 7,  
11, 23, 0, 5, 13, 3, 0, 29, 0, 31, 2, 0, 17, 0, 0, 37, 19, 13, 0, 41,  
7, 43, 0, 0, 23, 47, 0, 7, 5, 0, 13, 53, 3, 11, 0, 19, 29, 59, 0, 61,  
31, 0, 2, 0, 0, 67, 17, 0, 0, 71, 0



a(n), when not 0, appears to be the largest prime divisor of n,

are there any counter-examples to this observation ?
(my own investigation didn't find any out to n = 10,000)

if not, are there any number theorists that can shed any light on  
this curious phenomenon ?


thanks,
Peter Lawrence.