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A101744
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Triangular numbers which are 10-almost primes.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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.
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=1..27.
Eric Weisstein's World of Mathematics, Triangular Number.
Eric Weisstein's World of Mathematics, Almost Prime.
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FORMULA
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a(n) is in the intersection of {A000217} and {A046314}. Integers of the form k*(k+1)/2 which have exactly 10 prime factors.
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EXAMPLE
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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.
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MATHEMATICA
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BigOmega[n_Integer]:=Plus@@Last[Transpose[FactorInteger[n]]]; Select[Table[n*(n+1)/2, {n, 2, 5000}], BigOmega[ # ]?10&]
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CROSSREFS
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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
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post, Dec 14 2004
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STATUS
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approved
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