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 A101744 Triangular numbers which are 10-almost primes. 1
 32640, 73920, 130816, 165600, 204480, 265356, 294528, 401856, 592416, 839160, 947376, 990528, 1279200, 1445850, 1492128, 1606528, 1842240, 1844160, 2031120, 2049300, 2821500, 2956096, 3571128, 3963520, 4148640, 4250070, 4335040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A101745 contains the indices of this sequence, i.e. T(n) for what values of n are these 10-almost primes. Mathematica code and extension by Ray Chandler. REFERENCES Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 59, 1987. Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 33-38, 1996. Dudeney, H. E. Amusements in Mathematics. New York: Dover, pp. 67 and 167, 1970. LINKS Eric Weisstein's World of Mathematics, Triangular Number. Eric Weisstein's World of Mathematics, Almost Prime. FORMULA a(n) is in the intersection of {A000217} and {A046314}. Integers of the form k*(k+1)/2 which have exactly 10 prime factors. EXAMPLE a(1) = 32640 because that is the smallest triangular number which is also a 10-almost prime; specifically T(255) = 255*(255+1)/2 = 32640 = 2^7 * 3 * 5 * 17. MATHEMATICA BigOmega[n_Integer]:=Plus@@Last[Transpose[FactorInteger[n]]]; Select[Table[n*(n+1)/2, {n, 2, 5000}], BigOmega[ # ]?10&] CROSSREFS Cf. A000217, A046314, A068443, A075875, A076578-A076583, A075088, A101745. Sequence in context: A134949 A134947 A172700 * A013691 A152932 A075966 Adjacent sequences:  A101741 A101742 A101743 * A101745 A101746 A101747 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Dec 14 2004 STATUS approved

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