A083689 Numbers n such that the sum of the factorials of the digits of n! is prime.

2, 19, 24, 35, 40, 41, 42, 43, 73, 90, 125, 135, 180, 188, 209, 216, 217, 236, 241, 242, 267, 280, 304, 308, 321, 334, 343, 402, 409, 411, 436, 472, 475, 485, 487, 497, 572, 624, 635, 637, 647, 669, 689, 713, 751, 807, 844, 857, 902, 913, 930, 934, 947, 956