Numbers

n³ – 2n² – 51n + 737
= (n + 4)(n + 3)(n – 9) + 845

845 = 169×5

So, for the expression to be divisible by 169, (n + 4)(n + 3)(n – 9) should be divisible by 169

=> Either (n + 3) is divisible by 169 or (n + 4) is divisible by 13

So, n – 9 = 13, 26, 39, 52, 65, 78
=> n can be 22, 35, 48, 61, 74 and 87

So 6 possible values.