# Problem 386: Maximum length of an antichain

![graphic](img386.gif)

Let n be an integer and S(n) be the set of factors of n. A subset A of
S(n) is called an antichain of S(n) if A contains only one element or if
none of the elements of A divides any of the other elements of A. For
example: S(30) = {1, 2, 3, 5, 6, 10, 15, 30} {2, 5, 6} is not an
antichain of S(30). {2, 3, 5} is an antichain of S(30). Let N(n) be the
maximum length of an antichain of S(n). Find ΣN(n) for 1 ≤ n ≤ 108