Hi Mary,

One such number is 2^{12}. It's divisors are

1,2,2^{2},2^{3},2^{4},2^{5},2^{6},2^{7},2^{8},2^{9},2^{10},2^{11},2^{12},

i.e.

1,2,4,8,16,32,64,128,256,512,1024,2048,4096.

6^{12} doesn't work. 1,6,6^{2},...,6^{12} are divisors of 6^{12} but so is 3.

Is 2 special or would some other number raised to the 12 power work? What numbers raised to the 12 will work?

Penny

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