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6

Part of 2013 South East Mathematical Olympiad

Problems(1)

China South East Mathematical Olympiad 2013 problem 6

Source:

8/10/2013
n>1n>1 is an integer. The first nn primes are p1=2,p2=3,…,pnp_1=2,p_2=3,\dotsc, p_n. Set A=p1p1p2p2...pnpnA=p_1^{p_1}p_2^{p_2}...p_n^{p_n}. Find all positive integers xx, such that Ax\dfrac Ax is even, and Ax\dfrac Ax has exactly xx divisors
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