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A054531 Triangular array T read by rows: T(n,k) = n / GCD(n,k) (n >= 1, 1<=k<=n). 16
1, 2, 1, 3, 3, 1, 4, 2, 4, 1, 5, 5, 5, 5, 1, 6, 3, 2, 3, 6, 1, 7, 7, 7, 7, 7, 7, 1, 8, 4, 8, 2, 8, 4, 8, 1, 9, 9, 3, 9, 9, 3, 9, 9, 1, 10, 5, 10, 5, 2, 5, 10, 5, 10, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1, 12, 6, 4, 3, 12, 2, 12, 3, 4, 6, 12, 1, 13, 13, 13, 13, 13 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sum of n-th row = A057660(n). [Reinhard Zumkeller, Aug 12 2009]

Read as a linear sequence, this is conjectured to be the length of the shortest cycle of pebble-moves among the partitions of n (cf. A201144). - Andrew V. Sutherland, Nov 27 2011

The triangle of fractions A226314(i,j)/A054531(i,j) is an efficient way to enumerate the rationals [Fortnow]. - N. J. A. Sloane, Jun 09 2013

LINKS

Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened

Lance Fortnow, Counting the Rationals Quickly, Computational Complexity Weblog, Monday, March 01, 2004.

R. J. Mathar, Plots of cycle graphs of the finite groups up to order 36, (2015)

Yoram Sagher, Counting the rationals, Amer. Math. Monthly, 96 (1989), p. 823. Math. Rev. 90i:04001.

EXAMPLE

1;

2, 1;

3, 3, 1;

4, 2, 4, 1;

5, 5, 5, 5, 1;

6, 3, 2, 3, 6, 1;

7, 7, 7, 7, 7, 7, 1;

8, 4, 8, 2, 8, 4, 8, 1;

9, 9, 3, 9, 9, 3, 9, 9, 1;

10, 5,10, 5, 2, 5,10, 5,10, 1;

11,11,11,11,11,11,11,11,11,11, 1;

12, 6, 4, 3,12, 2,12, 3, 4, 6,12, 1;

13,13,13,13,13,13,13,13,13,13,13,13, 1;

PROG

(Haskell)

a054531 n k = div n $ gcd n k

a054531_row n = a054531_tabl !! (n-1)

a054531_tabl = zipWith (\u vs -> map (div u) vs) [1..] a050873_tabl

-- Reinhard Zumkeller, Jun 10 2013

CROSSREFS

Cf. A050873, A164306, A226314, A277227 (row reversed, k=0..n-1).

Sequence in context: A049834 A134625 A277227 * A207645 A263916 A115131

Adjacent sequences:  A054528 A054529 A054530 * A054532 A054533 A054534

KEYWORD

nonn,tabl,frac,easy

AUTHOR

N. J. A. Sloane, Apr 09 2000

STATUS

approved

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Last modified December 4 17:35 EST 2016. Contains 278755 sequences.