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Numbers n such that the sum of the factorials of the digits of n! is prime.
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%I #8 Nov 25 2018 13:24:43

%S 2,19,24,35,40,41,42,43,73,90,125,135,180,188,209,216,217,236,241,242,

%T 267,280,304,308,321,334,343,402,409,411,436,472,475,485,487,497,572,

%U 624,635,637,647,669,689,713,751,807,844,857,902,913,930,934,947,956

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

%e a(2)=19 because 19! = 121645100408832000

%e and 1!+2!+1!+6!+4!+5!+1!+0!+0!+4!+0!+8!+8!+3!+2!+0!+0!+0! = 81547 a prime.

%t Select[Range[1000],PrimeQ[Total[IntegerDigits[#!]!]]&] (* _Harvey P. Dale_, Nov 25 2018 *)

%K base,nonn

%O 1,1

%A _Jason Earls_, Jun 15 2003