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A054531 Triangular array T read by rows: T(n,k) = n / GCD(n,k) (n >= 1, 1<=k<=n). 13
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). [From 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

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, http://blog.computationalcomplexity.org/2004/03/counting-rationals-quickly.html

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

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Last modified September 17 09:38 EDT 2014. Contains 246836 sequences.