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EXAMPLE
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a(3) = 12 since for n = 3 the tuples forming the solutions of 1 = 1/x_1 + 1/x_2 + 1/x_3 are (x_1, x_2, x_3) in {(2, 3, 6), (2, 4, 4), (3, 3, 3)}. All these terms combined have an lcm of 12. The ways to write 12 as a sum of 3 of its divisors are therefore 12 = 12/2 + 12/3 + 12/6 = 6 + 4 + 2. Similarily we have 12 = 6 + 3 + 3 and 12 = 4 + 4 + 4.
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