A109101 Numbers n such that n! is the product of exactly 3 smaller factorials (greater than 1).
576, 1152, 2304, 2880, 3456, 4608, 5760, 6912, 9216, 11520, 18432, 20736, 23040, 36864, 41472, 46080, 73728, 92160
Offset: 1
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34560! = 2! * 3! * 4! * 5! * 34559!, using five different factorials, so a(5)=34560.
10! = 3! * 5! * 7!, so 10 is in the sequence.