If n is one of these numbers, the only odd numbers in the nth row of Pascal's triangle are the ones at the ends. One can tell whether a non-increasing non-negative series a-sub-n converges by looking at its values when n is one of these numbers, according to Cauchy's condensation test. The only currently known perfect numbers can each be written as a large prime times one 
If n is one of these numbers, the only odd numbers in the nth row of Pascal's triangle are the ones at the ends. One can tell whether a non-increasing non-negative series a-sub-n converges by looking at its values when n is one of these numbers, according to Cauchy's condensation test. The only currently known perfect numbers can each be written as a large prime times one of these numbers. The size of the power set of a finite set is a number of this type. Adding one to a (*) Mersenne prime always gives one of these numbers. They are the number of vertices of an n-dimensional hypercube, and the binary representation of these numbers have only one 1 in them. For 10 points, identify these numbers, like 16, 32, and 128, which are formed by exponentiating the smallest prime.