A242868 Numbers n such that sum of the factorial of digits of n is semiprime.

3, 14, 15, 16, 17, 18, 22, 24, 25, 27, 28, 40, 41, 42, 50, 51, 52, 60, 61, 70, 71, 72, 80, 81, 82, 102, 104, 105, 107, 108, 112, 114, 115, 117, 118, 120, 121, 123, 125, 126, 128, 132, 140, 141, 144, 145, 146, 147, 148, 150, 151, 152, 154, 156, 157, 158, 162, 164

Offset: 1

Author

K. D. Bajpai, May 24 2014

Keywords

• nonn
• base

Examples

			a(4) = 16:  1! + 6! = 1 + 720 = 721 = 7 * 103 which is semiprime.
a(9) = 25:  2! + 5! = 2 + 120 = 122 = 2 * 61 which is semiprime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A061602, A165451.

Programs

Maple

with(numtheory):A242868:= proc() local a; a:=add( i!,i = convert((n), base, 10))(n);if bigomega(a)=2 then RETURN (n);fi; end: seq(A242868 (), n=1..300);

Mathematica

Select[Range[200],PrimeOmega[Total[IntegerDigits[#]!]]==2&] (* Harvey P. Dale, Jul 30 2015 *)