Please reason step by step, and put your final answer within \boxed{}.
Let the positive divisors of the natural number \( n \) be \( 1 = d_1 < d_2 < \ldots < d_k = n \). Determine all \( n \) for which the following holds:

\[ 
2n = d_5^2 + d_6^2 - 1
\]
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