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

Author

K. D. Bajpai, May 24 2014

Keywords

• nonn
• base

Comments

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

Intersection of A000217 and A242868.

Examples

			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.
		

Links

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

Crossrefs

Cf. A001358, A000217, A061602, A242868.

Programs

Maple

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);

Mathematica

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 *)