

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
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OFFSET

1,2


COMMENTS

Sum of nth 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 pebblemoves 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 !! (n1)
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..n1).
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



