login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054531 Triangular array T read by rows: T(n,k) = n / GCD(n,k) (n >= 1, 1<=k<=n). 14
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.

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.

Sequence in context: A219158 A049834 A134625 * A207645 A115131 A210258

Adjacent sequences:  A054528 A054529 A054530 * A054532 A054533 A054534

KEYWORD

nonn,tabl,frac,easy

AUTHOR

N. J. A. Sloane, Apr 09 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 22 16:20 EST 2014. Contains 249807 sequences.