A242897 Catalan numbers C(n) such that sum of the factorials of digits of C(n) is semiprime.
14, 42, 132, 4862, 35357670, 1767263190, 91482563640, 4861946401452, 212336130412243110, 2622127042276492108820, 10113918591637898134020, 39044429911904443959240, 116157871455782434250553845880, 6852456927844873497549658464312, 368479169875816659479009042713546950
Offset: 1
Examples
a(2) = 42 = (2*5)!/(5!*(5+1)!) is 5th Catalan number: 4!+2! = 26 = 2 * 13 which is semiprime. a(4) = 4862 = (2*9)!/(9!*(9+1)!) is 9th Catalan number: 4!+8!+6!+2! = 41066 = 2 * 20533 which is semiprime.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..347
Programs
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Maple
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);
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Mathematica
Select[CatalanNumber[Range[70]],PrimeOmega[Total[IntegerDigits[#]!]]==2&] (* Harvey P. Dale, Dec 13 2022 *)
Comments