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A007622
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Consider Leibniz's harmonic triangle (A003506) and look at the non-boundary terms. Sequence gives numbers appearing in denominators, sorted.
(Formerly M4096)
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11
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6, 12, 20, 30, 42, 56, 60, 72, 90, 105, 110, 132, 140, 156, 168, 182, 210, 240, 252, 272, 280, 306, 342, 360, 380, 420, 462, 495, 504, 506, 552, 600, 630, 650, 660, 702, 756, 812, 840, 858, 870, 930, 992, 1056, 1092, 1122, 1190, 1260, 1320, 1332
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OFFSET
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1,1
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COMMENTS
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No term is prime, about 80% are abundant, but the first few deficient are: 105, 110, 182, 495, 506, 1365, 1406, 1892, 2162, 2756, 2907, 3422, 3782, 4556, 5313, ..., . [From Robert G. Wilson v, Aug 16 2010]
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 83, Problem 25.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 35.
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LINKS
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_Robert G. Wilson v_, Table of n, a(n) for n = 1..1217.
Eric Weisstein's World of Mathematics, Leibniz Harmonic Triangle.
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MATHEMATICA
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L[n_, 1] := 1/n; L[n_, m_] := L[n, m] = L[n - 1, m - 1] - L[n, m - 1]; Take[ Union[ Flatten[ Table[ 1/L[n, m], {n, 3, 150}, {m, 2, Floor[n/2 + .5]}]]], 65]
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CROSSREFS
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Sequence in context: A083209 A080714 A116368 * A180291 A056930 A064971
Adjacent sequences: A007619 A007620 A007621 * A007623 A007624 A007625
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein (mira(AT)math.berkeley.edu)
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Jul 25 2000. Rechecked Jun 27 2003.
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STATUS
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approved
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