%I
%S 32640,73920,130816,165600,204480,265356,294528,401856,592416,839160,
%T 947376,990528,1279200,1445850,1492128,1606528,1842240,1844160,
%U 2031120,2049300,2821500,2956096,3571128,3963520,4148640,4250070,4335040
%N Triangular numbers which are 10almost primes.
%C A101745 contains the indices of this sequence, i.e. T(n) for what values of n are these 10almost primes. Mathematica code and extension by _Ray Chandler_.
%D Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 59, 1987.
%D Conway, J. H. and Guy, R. K. The Book of Numbers. New York: SpringerVerlag, pp. 3338, 1996.
%D Dudeney, H. E. Amusements in Mathematics. New York: Dover, pp. 67 and 167, 1970.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TriangularNumber.html">Triangular Number</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.
%F a(n) is in the intersection of {A000217} and {A046314}. Integers of the form k*(k+1)/2 which have exactly 10 prime factors.
%e a(1) = 32640 because that is the smallest triangular number which is also a 10almost prime; specifically T(255) = 255*(255+1)/2 = 32640 = 2^7 * 3 * 5 * 17.
%t BigOmega[n_Integer]:=Plus@@Last[Transpose[FactorInteger[n]]]; Select[Table[n*(n+1)/2, {n, 2, 5000}], BigOmega[ # ]?10&]
%Y Cf. A000217, A046314, A068443, A075875, A076578A076583, A075088, A101745.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Dec 14 2004
