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Search: id:A110493
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| A110493 |
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Largest prime p such that p^2 divides binomial(2n,n), or 0 if binomial(2n,n) is squarefree. |
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2
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| 0, 0, 2, 0, 3, 2, 2, 3, 2, 2, 2, 2, 5, 5, 3, 3, 3, 5, 5, 3, 2, 2, 5, 5, 7, 7, 7, 2, 2, 2, 2, 7, 7, 7, 3, 2, 2, 5, 7, 7, 7, 3, 5, 5, 3, 7, 7, 7, 5, 3, 3, 3, 3, 2, 2, 3, 2, 2, 3, 3, 11, 11, 11, 11, 11, 5, 5, 5, 5, 5, 5, 11, 11, 11, 11, 11, 3, 5, 5, 3, 7, 7, 11, 11, 13, 13, 13, 13, 13, 13, 5, 5, 5, 11, 11
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Binomial(2n,n) is squarefree for only n=1,2,4. Sequence A059097 lists n such that a(n)=0 or 2. The plot shows the quadratic nature of this sequence for n<15000. Sequence A110494 make the quadratic behavior clearer.
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LINKS
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T. D. Noe, Plot of A110493
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EXAMPLE
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a(5)=3 because binomial(10,5) = 252 = 2^2 3^2 7.
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MATHEMATICA
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Table[f=FactorInteger[Binomial[2n, n]]; s=Select[f, #[[2]]>1&]; If[s=={}, 0, s[[ -1, 1]]], {n, 100}]
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CROSSREFS
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Cf. A110494 (least k such that prime(n)^2 divides binomial(2k, k)).
Sequence in context: A100949 A152164 A157927 this_sequence A118234 A152039 A132623
Adjacent sequences: A110490 A110491 A110492 this_sequence A110494 A110495 A110496
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jul 22 2005
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