Most numbers have interesting properties, if you look hard enough and interpret “interesting” liberally. Let’s choose a number at random—300, say—and list some of its properties:
- It is divisible by the square of its largest prime factor.
- It is the area of a triangle with integer sides and integer area
- It is a folding point of the non-negative integers written in a hexagonal spiral (see below), as are 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, etc.
A number that shares these properties is 108: (a) It is divisible by 9, or the square of its largest prime factor (3), (b) it is the area of a triangle with sides 15, 15, and 18, and (c) it is a folding point of the hexagon (it would be to the right of 75 in the hexagon below).
Write a function to determine whether a number has the three properties listed above.
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To pass the test cases, it seems that only conditions 1 and 3 need to be checked.
I've added some test cases. For example, the value in Test 3 (200) satisfies the first and third conditions but not the second.