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A054531
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Triangular array T read by rows: T(n,k) = n / GCD(n,k) (n >= 1, 1<=k<=n).
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12
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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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table;
graph;
refs;
listen;
history;
text;
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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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
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EXAMPLE
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1; 2,1; 3,3,1; 4,2,4,1; 5,5,5,5,1; ...
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PROG
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(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
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CROSSREFS
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Cf. A050873, A164306, A226314.
Sequence in context: A219158 A049834 A134625 * A207645 A115131 A210258
Adjacent sequences: A054528 A054529 A054530 * A054532 A054533 A054534
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KEYWORD
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nonn,tabl,frac,easy,changed
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AUTHOR
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N. J. A. Sloane, Apr 09 2000
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STATUS
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approved
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