A184481 Semiprime centered triangular numbers.

4, 10, 46, 85, 166, 235, 274, 361, 514, 694, 901, 1135, 1219, 1306, 1585, 1891, 2461, 2839, 3106, 3385, 3826, 3979, 4135, 5311, 5674, 6049, 6241, 6835, 7246, 8551, 9481, 10966, 11485, 11749, 12286, 12559, 13969, 15151, 15454, 17335, 18649, 18985, 19666, 21421, 21781, 22879, 23626, 24385, 26734, 27949, 28774, 30034, 32194, 33079, 33526

Offset: 1

Author

Jonathan Vos Post, Feb 12 2011

Keywords

• nonn
• easy

Comments

Numbers of the form 3*n*(n-1)/2 + 1 = p*q where p and q are primes, not necessarily distinct. This is to semiprimes A001358 as A125602 is to primes A000040.

Examples

			a(3) = 3*6(6-1)/2 + 1 = 10 = 2 * 5.
		

Crossrefs

Cf. A001358, A005448, A125602.

Programs

Mathematica

SemiprimeQ[n_] := Total[FactorInteger[n]][[2]] == 2; Select[Table[3*n (n - 1)/2 + 1, {n, 150}], SemiprimeQ]
Select[Table[(3n(n-1))/2+1,{n,200}],PrimeOmega[#]==2&] (* Harvey P. Dale, May 13 2012 *)

Formula

A001358 INTERSECTION A005448.