6

Part of 2004 Junior Tuymaada Olympiad

Problems(1)

pos. integer with integer sum of the reciprocals of all its natural divisors

Source: Tuymaada Junior 2004 p6

We call a positive integer good if the sum of the reciprocals of all its natural divisors are integers. Prove that if

m

is a good number, and

p> m

is a prime number, then

pm

number theorySumreciprocal sumpositive integersprime