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%I #16 Feb 21 2023 10:46:15
%S 6,28,36,120,136,171,276,300,325,528,561,780,820,903,1081,1128,1176,
%T 1275,1540,1596,1653,2080,2211,2415,2485,2556,2775,3160,3240,3403,
%U 3655,3828,4371,4851,5151,5253,5356,5460,5995,6105,6328,6441,6903,7381,7503,8001,8256
%N Triangular numbers T such that T-2 is semiprime.
%C The n-th triangular number T(n) = n*(n+1)/2.
%C Triangular numbers of the form p*q + 2, where p and q are primes (not necessarily distinct).
%H K. D. Bajpai and N. J. A. Sloane, <a href="/A242344/b242344.txt">Table of n, a(n) for n = 1..27939</a> [First 10000 terms from K. D. Bajpai]
%e a(2) = 28 = 7*(7+1)/2 = 28 - 2 = 26 = 2 * 13 is semiprime.
%e a(3) = 36 = 8*(8+1)/2 = 36 - 2 = 34 = 2 * 17 is semiprime.
%p with(numtheory): A242344:= proc()local t; t:=x*(x+1)/2;if bigomega(t-2)=2 then RETURN (t); fi;end: seq(A242344(),x=1..200);
%t Select[Table[n*(n + 1)/2, {n, 200}], PrimeOmega[# - 2] == 2 &]
%t Select[Accumulate[Range[200]],PrimeOmega[#-2]==2&] (* _Harvey P. Dale_, Feb 21 2023 *)
%Y Cf. A001358, A000217, A063637, A063638.
%K nonn
%O 1,1
%A _K. D. Bajpai_, May 11 2014
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