形如p^kp-1的非优美指数

摘要

利用除数函数的性质，证明了若素数p≥11，正整数k满足1≤k≤（p-3）p，则p^kp-1为非优美指数，存在无穷多个非优美指数，再次否定了A.Murthy猜想。%Abstract： We studied the non-beauty indexes by property of divisor function. Ifp≥ 11 is a prime and k is a positive integer satisfying 1 ≤ k ≤ （p-3）p, thenp^kp-1 is not an index of beauty. There are infinitely many positive integer which is not an index of beauty, therefore the conjecture of A.Murthy is negative.