A007622 Consider Leibniz's harmonic triangle (A003506) and look at the non-boundary terms. Sequence gives numbers appearing in denominators, sorted. (Formerly M4096)

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

Offset

1,1

Comments

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, .... - Robert G. Wilson v, Aug 16 2010

A002943 = (6, 20, 42, 72, 110, 156, 210, 272, 342, 420, 506, 600, 702, ...) is a subsequence: indeed, this is every second denominator of the first differences of the sequence 1/n. - M. F. Hasler, Oct 11 2015

References

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.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..1217.

Eric Weisstein's World of Mathematics, Leibniz Harmonic Triangle.

Mathematica

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]
t[n_, k_] := Denominator[n!*k!/(n + k + 1)!]; Take[ DeleteDuplicates@ Rest@ Sort@ Flatten@ Table[t[n - k, k], {n, 2, 150}, {k, n/2 + 1}], 65] (* Robert G. Wilson v, Jun 12 2014 *)

Crossrefs

Sequence in context: A116368 A343065 A290467 * A180291 A056930 A326378

Adjacent sequences: A007619 A007620 A007621 * A007623 A007624 A007625

Keyword

nonn

Author

N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jul 25 2000. Rechecked Jun 27 2003.

Status

approved