A242344 Triangular numbers T such that T-2 is semiprime.

6, 28, 36, 120, 136, 171, 276, 300, 325, 528, 561, 780, 820, 903, 1081, 1128, 1176, 1275, 1540, 1596, 1653, 2080, 2211, 2415, 2485, 2556, 2775, 3160, 3240, 3403, 3655, 3828, 4371, 4851, 5151, 5253, 5356, 5460, 5995, 6105, 6328, 6441, 6903, 7381, 7503, 8001, 8256

Offset: 1

Author

K. D. Bajpai, May 11 2014

Keywords

• nonn

Comments

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

Triangular numbers of the form p*q + 2, where p and q are primes (not necessarily distinct).

Examples

			a(2) = 28 = 7*(7+1)/2 = 28 - 2 = 26 = 2 * 13 is semiprime.
a(3) = 36 = 8*(8+1)/2 = 36 - 2 = 34 = 2 * 17 is semiprime.
		

Links

• K. D. Bajpai and N. J. A. Sloane, Table of n, a(n) for n = 1..27939 [First 10000 terms from K. D. Bajpai]

Crossrefs

Cf. A001358, A000217, A063637, A063638.

Programs

Maple

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);

Mathematica

Select[Table[n*(n + 1)/2, {n, 200}], PrimeOmega[# - 2] == 2 &]
Select[Accumulate[Range[200]],PrimeOmega[#-2]==2&] (* Harvey P. Dale, Feb 21 2023 *)