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%I #31 May 26 2014 21:57:23
%S 3,15,28,105,120,171,210,231,406,561,741,820,990,1081,1275,1378,1485,
%T 1540,1596,1953,2211,2485,2775,3003,3240,3321,3741,3916,4005,4371,
%U 4560,4851,5460,6105,6903,7381,7750,8001,8128,8515,9316,9591,9730,10153,10440,10878
%N Triangular numbers T such that sum of the factorials of digits of T is semiprime.
%C The n-th triangular number T(n) = n * (n+1)/2.
%C Intersection of A000217 and A242868.
%H K. D. Bajpai, <a href="/A242571/b242571.txt">Table of n, a(n) for n = 1..10000</a>
%e 18*(18+1)/2 = 171 is triangular number. 1! + 7! + 1! = 5042 = 2 * 2521 is semiprime. Hence 171 is in the sequence.
%e 28*(28+1)/2 = 406 is triangular number. 4! + 0! + 6! = 745 = 5 * 149 is semiprime. Hence 406 is in the sequence.
%p 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);
%t 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 *)
%Y Cf. A001358, A000217, A061602, A242868.
%K nonn,base
%O 1,1
%A _K. D. Bajpai_, May 24 2014
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