A242868 -id:A242868 - cp's OEIS frontend

A242571 Triangular numbers T such that sum of the factorials of digits of T is semiprime.

3, 15, 28, 105, 120, 171, 210, 231, 406, 561, 741, 820, 990, 1081, 1275, 1378, 1485, 1540, 1596, 1953, 2211, 2485, 2775, 3003, 3240, 3321, 3741, 3916, 4005, 4371, 4560, 4851, 5460, 6105, 6903, 7381, 7750, 8001, 8128, 8515, 9316, 9591, 9730, 10153, 10440, 10878

Offset: 1

K. D. Bajpai, May 24 2014

The n-th triangular number T(n) = n * (n+1)/2.

Intersection of A000217 and A242868.

			18*(18+1)/2 = 171 is triangular number. 1! + 7! + 1! = 5042 = 2 * 2521 is semiprime. Hence 171 is in the sequence.
28*(28+1)/2 = 406 is triangular number. 4! + 0! + 6! = 745 = 5 * 149 is semiprime. Hence 406 is in the sequence.

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

Cf. A001358, A000217, A061602, A242868.

with(numtheory): A242571= proc() if bigomega(add( i!,i = convert((n*(n+1)/2), base, 10))(n*(n+1)/2))=2 then RETURN (n*(n+1)/2);fi; end: seq(A242571 (),n=1..300);

fQ[n_] := PrimeOmega[ Total[ IntegerDigits[ n (n + 1)/2]!]] == 2; s = Select[ Range@ 160, fQ@# &]; s (s + 1)/2 (* Robert G. Wilson v, May 26 2014 *)

A242897 Catalan numbers C(n) such that sum of the factorials of digits of C(n) is semiprime.

Original entry on oeis.org

14, 42, 132, 4862, 35357670, 1767263190, 91482563640, 4861946401452, 212336130412243110, 2622127042276492108820, 10113918591637898134020, 39044429911904443959240, 116157871455782434250553845880, 6852456927844873497549658464312, 368479169875816659479009042713546950

Offset: 1

K. D. Bajpai, May 25 2014

The n-th Catalan number is C(n) = (2*n)!/(n!*(n+1)!).
a(347), having 998 digits, is the last term in b-file.
a(348) has 1003 digits, hence is not included in b-file.
Intersection of A000108 and A242868.

			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.

K. D. Bajpai, Table of n, a(n) for n = 1..347

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

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);

Select[CatalanNumber[Range[70]],PrimeOmega[Total[IntegerDigits[#]!]]==2&] (* Harvey P. Dale, Dec 13 2022 *)

cp's OEIS Frontend

A242571 Triangular numbers T such that sum of the factorials of digits of T is semiprime.

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