A242897 - OEIS

%I #14 Dec 13 2022 17:59:59

%S 14,42,132,4862,35357670,1767263190,91482563640,4861946401452,

%T 212336130412243110,2622127042276492108820,10113918591637898134020,

%U 39044429911904443959240,116157871455782434250553845880,6852456927844873497549658464312,368479169875816659479009042713546950

%N Catalan numbers C(n) such that sum of the factorials of digits of C(n) is semiprime.

%C The n-th Catalan number is C(n) = (2*n)!/(n!*(n+1)!).

%C a(347), having 998 digits, is the last term in b-file.

%C a(348) has 1003 digits, hence is not included in b-file.

%C Intersection of A000108 and A242868.

%H K. D. Bajpai, <a href="/A242897/b242897.txt">Table of n, a(n) for n = 1..347</a>

%e a(2) = 42 = (2*5)!/(5!*(5+1)!) is 5th Catalan number: 4!+2! = 26 = 2 * 13 which is semiprime.

%e a(4) = 4862 = (2*9)!/(9!*(9+1)!) is 9th Catalan number: 4!+8!+6!+2! = 41066 = 2 * 20533 which is semiprime.

%p with(numtheory): A242897:= proc() if bigomega(add( i!,i = convert(((2*n)!/(n!*(n+1)!)), base, 10))((2*n)!/(n!*(n+1)!)))=2  then RETURN ((2*n)!/(n!*(n+1)!)); fi; end: seq(A242897 (), n=1..100);

%t Select[CatalanNumber[Range[70]],PrimeOmega[Total[IntegerDigits[#]!]]==2&] (* _Harvey P. Dale_, Dec 13 2022 *)

%Y Cf. A000108, A001358, A061602, A242855, A242868.

%K nonn,base,less

%O 1,1

%A _K. D. Bajpai_, May 25 2014