# 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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