5597 has a cube with only odd digits (A030099 and A085597): 55973 = 175,333,911,173.
5597 is the number of binary rooted trees with 16 nodes and height exactly 8 (A036597).
5597 is a composite number n such that every divisor (except 1) of n contains the digit 9 (A062680).
5597 has two representations as a sum of two squares: 5597 = 112 + 742 = 462 + 592.
5597 is the hypotenuse of two primitive Pythagorean triples: 55972 = 13652 + 54282 = 16282 + 53552.
5597 is a divisor of 1224 - 1.
Source: What's Special About This Number?
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