

A054531


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


12



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). [From 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
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/countingrationalsquickly.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 !! (n1)
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,changed


AUTHOR

N. J. A. Sloane, Apr 09 2000


STATUS

approved



