1, 4, 8, 9, 16, 25, 27, 32

Find the largest positive integer n<100,n<100, such that there exists an arithmetic progression of positive integers a1,a2,...,ana_1,a_2,...,a_n with the following properties.

1) All numbers a2,a3,...,an1a_2,a_3,...,a_{n-1} are powers of positive integers, that is numbers of the form jk,j^k, where j1j\geq 1 and k2k\geq 2 are integers.

2) The numbers a1a_1 and ana_{n} are not powers of positive integers.

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