The numbers are: 93+95+97 = 285
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Can't be done. The number has to be a multiple of 3.
No two consecutive numbers have a product that is an even number. Any two consecutive numbers include one odd number and one even number. The product of one odd number and one even number is always an odd number.
Divide the sum of the three consecutive odd integers by 3: -3 /3 = -1. The smallest of these integers will be two less than -1 and the largest will be two more than -1, so the three consecutive odd integers will be -3, -1, and +1.
After (3, 5, 7), you can't have any more such "triplets", since one of the three must needs be a multiple of 3.
-33 + -33 + -29 = -93