Representations of 100

Find the number of way to represent \(100\) as a sum of distinct positive integers that are not divisible by primes strictly greater than \(3\).

Details and assumptions

Clarification: The order of the summands does not matter, but they must be distinct. For example, \(6\) can be represented in this manner in three different ways: \(1+2+3,\ 2+4,\ 6\). The sum \(1+1+4\) does not count because the summands are not distinct.

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