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Search: id:A027750
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| A027750 |
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Triangle read by rows in which row n list the divisors of n. |
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51
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| 1, 1, 2, 1, 3, 1, 2, 4, 1, 5, 1, 2, 3, 6, 1, 7, 1, 2, 4, 8, 1, 3, 9, 1, 2, 5, 10, 1, 11, 1, 2, 3, 4, 6, 12, 1, 13, 1, 2, 7, 14, 1, 3, 5, 15, 1, 2, 4, 8, 16, 1, 17, 1, 2, 3, 6, 9, 18, 1, 19, 1, 2, 4, 5, 10, 20, 1, 3, 7, 21, 1, 2, 11, 22, 1, 23, 1, 2, 3, 4, 6, 8, 12, 24, 1, 5, 25, 1, 2, 13, 26, 1, 3, 9, 27, 1, 2, 4, 7, 14, 28, 1, 29
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Or, in the list of natural numbers (A000027), replace n by its divisors.
This gives the first elements of the ordered pairs (a,b) a >= 1, b >= 1 ordered by their product ab.
Also, row n lists the largest parts of the partitions of n whose parts are not distinct. [From Omar E. Pol (info(AT)polprimos.com), Sep 17 2008]
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LINKS
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Franklin T. Adams-Watters, Rows 1 ... 1000, flattened
Franklin T. Adams-Watters, Rows 1 to 10000
Eric Weisstein's World of Mathematics, Divisor
O. E. Pol, A shell model of partitions [From Omar E. Pol (info(AT)polprimos.com), Sep 17 2008]
O. E. Pol, A 3D model of the divisors of the natural numbers [From Omar E. Pol (info(AT)polprimos.com), Oct 22 2009]
O. E. Pol, Illustration of initial terms [From Omar E. Pol (info(AT)polprimos.com), Oct 22 2009]
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FORMULA
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a(A006218(n-1) + k) = k-divisor of n, 1<=k<=A000005(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 10 2006
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EXAMPLE
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1; 1,2; 1,3; 1,2,4; 1,5; 1,2,3,6; ...
[From Omar E. Pol (info(AT)polprimos.com), Sep 17 2008]
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MATHEMATICA
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Flatten[ Table[ Flatten [ Divisors[ n ] ], {n, 1, 30} ] ]
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PROGRAM
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(MAGMA) [Divisors(n) : n in [1..20]];
(Other) sage: [divisors(n) for n in xrange(1, 30)] # view:[[1], [1, 2], [1, 3], [1, 2, 4], [1, 5], [1, 2, 3, 6], [1, 7], [1, 2, 4, 8], [1, 3, 9], [1, 2, 5, 10], [1, 11], [1, 2, 3, 4, 6, 12], [1, 13], [1, 2, 7, 14], [1, 3, 5, 15], etc... [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 24 2009]
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CROSSREFS
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Cf. A056534, A056538, A027751.
Cf. A135010, A138121. [From Omar E. Pol (info(AT)polprimos.com), Sep 17 2008]
A161700. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 17 2009]
Cf. A000005, A163280. [From Omar E. Pol (info(AT)polprimos.com), Oct 22 2009]
Adjacent sequences: A027747 A027748 A027749 this_sequence A027751 A027752 A027753
Sequence in context: A165416 A057059 A162306 this_sequence A087295 A130517 A056951
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KEYWORD
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nonn,easy,tabf,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)
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