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Search: id:A121612
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| A121612 |
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Numbers n such that bigomega of n-th Catalan number divides n. |
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+0
1
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| 2, 3, 4, 8, 10, 12, 16, 20, 22, 117, 408, 432, 444, 492, 504, 508, 1555, 1560, 1605, 1675, 1790, 5832, 5940, 5976, 6048, 6078, 6102, 6108, 6132, 6138, 21175, 21266, 21280, 21301, 21434, 21462, 21469, 21616, 21623, 21749, 21770, 21784
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The number of prime divisors of n-th Catalan number (counted with multiplicity) divides n.
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FORMULA
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{n such that A081399(n)|n} = {n such that A001222[A000108(n)]|n}.
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EXAMPLE
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a(1) = 2 because bigomega(Catalan(2)) = bigomega(2) = 1 and 1 | 2.
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MATHEMATICA
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fQ[n_] := Mod[n, Plus @@ (Last@# & /@ FactorInteger[ Binomial[2n, n]/(n + 1)])] == 0; s = {}; Do[ If[fQ@n, Print@n; AppendTo[s, n]], {n, 2, 35500}] - Robert G. Wilson v Sep 11 2006
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CROSSREFS
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Cf. A000108, A001222, A081399.
Sequence in context: A047456 A073465 A161494 this_sequence A061193 A135772 A051783
Adjacent sequences: A121609 A121610 A121611 this_sequence A121613 A121614 A121615
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 08 2006
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EXTENSIONS
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Corrected and extended (a(10)-a(42)) by Robert G. Wilson v Sep 11 2006
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