%I A068443
%S A068443 6,10,15,21,55,91,253,703,1081,1711,1891,2701,3403,5671,12403,13861,
%T A068443 15931,18721,25651,34453,38503,49141,60031,64261,73153,79003,88831,
%U A068443 104653,108811,114481,126253,146611,158203,171991,188191,218791,226801
%N A068443 Triangular numbers which are the product of two primes.
%C A068443 These triangular numbers are equal to p * (2p +/- 1).
%C A068443 All a(n) belong to A006987(n) = {6, 10, 15, 20, 21, 28, 35, 36, 45, 55, 
               56, 66, 70, 78, 84, 91, ...} Binomial coefficients: C(n,k), 2 <= 
               k <= n-2. For n>2 all a(n) are odd and belong to A095147(n) = {15, 
               21, 35, 45, 55, 91, 105, 153, 165, 171, 231, 253, ...} Odd binomial 
               coefficients: C(n,k), 2 <= k <= n-2. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Oct 31 2006
%C A068443 A156592 is a subsequence. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Feb 10 2009]
%C A068443 A010054(a(n))*A064911(a(n)) = 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Dec 03 2009]
%H A068443 T. D. Noe, <a href="b068443.txt">Table of n, a(n) for n=1..1000</a>
%e A068443 0,1,3,6,10,... 6=2*3; 2 and 3 are two distinct primes, 10=2*5; 2 and 
               5 are two distinct primes, ... - Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Feb 27 2009
%e A068443 a(11) = 1891 and 1891 = 31 * 61
%t A068443 Select[ Table[ n(n + 1)/2, {n, 700}], Apply[Plus, Transpose[ FactorInteger[ 
               # ]] [[2]]] == 2 &].
%Y A068443 Cf. A000217, A005382 & A005384.
%Y A068443 Cf. A006987, A095147.
%Y A068443 Cf. A001358, A005385, A006881, A007304, A066179, A111206, A157342, A157344, 
               A157345, A157346, A157347, A157352, A157353, A157354, A157355, A157356, 
               A157357. - Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 27 2009
%Y A068443 Sequence in context: A115744 A122783 A124000 this_sequence A113940 A099981 
               A022949
%Y A068443 Adjacent sequences: A068440 A068441 A068442 this_sequence A068444 A068445 
               A068446
%K A068443 easy,nonn,new
%O A068443 1,1
%A A068443 Stephan Wagler (stephanwagler(AT)aol.com), Mar 09 2002
%E A068443 Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 08 2002
%E A068443 Definition corrected by Zak Seidov, Mar 09 2008