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%I #7 May 19 2014 02:36:07
%S 6,15,28,36,45,55,78,91,105,136,153,171,190,231,253,276,325,351,406,
%T 465,528,630,703,780,820,861,1035,1081,1176,1225,1275,1431,1540,1596,
%U 1653,1711,1770,2016,2080,2211,2346,2701,2775,2850,3003,3160,3240,3321,3403
%N Triangular numbers T such that sum of digits of T is semiprime.
%C The n-th triangular number T(n) = n*(n+1)/2.
%C Triangular numbers with digital sum = p * q, where p and q are primes.
%H K. D. Bajpai, <a href="/A242454/b242454.txt">Table of n, a(n) for n = 1..10000</a>
%e a(2) = 15 = 5*(5+1)/2: 1+5 = 6 = 2 * 3 is semiprime.
%e a(3) = 28 = 7*(7+1)/2: 2+8 = 10 = 2 * 5 is semiprime.
%p with(numtheory): A242454:= proc()local a,b; a:=x*(x+1)/2; b:=add( i,i = convert((a), base, 10))(a); if bigomega(b)=2 then RETURN (a); fi; end: seq(A242454 (), x=1..100);
%t Select[Table[n*(n+1)/2, {n, 200}], PrimeOmega[Sum[DigitCount[#][[i]]*i, {i,1,9}]] == 2 &]
%Y Cf. A000217, A001358, A158195, A118688, A242343.
%K nonn,base,less
%O 1,1
%A _K. D. Bajpai_, May 15 2014