# Ryan's Poly-Sum-Deficiency?

The aliquot sum $$s(n)$$ of a natural number $$n$$ is the sum of its proper divisors; in other words, the sum of its divisors subtracted by $$n$$. For example, $$s(6) = 1+2+3 = 6$$.

A natural number $$n$$ is deficient if $$s(n) < n$$. For example, $$6$$ is not deficient since $$s(6) = 6 \ge 6$$, but $$8$$ is deficient since $$s(8) = 7 < 8$$.

A natural number $$n$$ is triangular if there exists a natural number $$m$$ such that $$n = \frac{m(m+1)}{2}$$. Note that $$0$$ is not considered triangular.

A natural number $$n$$ is a 3-Ryan number if both $$n$$ and $$s(n)$$ are distinct triangular numbers. For example, $$3$$ is a 3-Ryan number since $$3$$ and $$s(3) = 1$$ are distinct triangular numbers, but $$6$$ isn't since $$6$$ and $$s(6) = 6$$ are not distinct, $$10$$ isn't since $$s(10) = 8$$ is not a triangular number, and $$4$$ isn't since $$4$$ is not a triangular number.

Determine the 7th smallest deficient 3-Ryan number.

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