Find a set of 10 numbers such that all pairs have a different GCF The set of ten numbers below:

223092870
17237308840522
1075474925835771
12574206406402195
79458974087499419
265057843710517649
466012798920390527
926434345611831877
1390237791335182649
2336970054109245767


has the property that no two pairs of numbers have the same greatest common factor. (In this case, the greatest common factor of each pair of numbers is actually a distinct prime.)

Your task is to find the set of 10 positive integers with the smallest sum that satisfy this property.

For reference, the sum of the above ten numbers is 5 477 838 726 638 839 246 (&approx;5.48&times;1018).
Sum: 58025

(ruby)

(0..9).map{|i|(2**i)*(3**(9-i))}


Gives

[19683, 13122, 8748, 5832, 3888, 2592, 1728, 1152, 768, 512]