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A081387
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Number of non-unitary prime divisors of central binomial coefficient, C(2n,n) = A000984(n), i.e., number of prime factors in C(2n,n) whose exponent is greater than one.
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9
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0, 0, 1, 0, 2, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 2, 2, 2, 2, 1, 1, 3, 3, 3, 3, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 4, 3, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 3, 3, 3, 2, 4, 2, 2, 3, 3, 3, 3, 4, 4, 5, 4, 4, 2, 3, 3, 2, 2, 2, 4, 3, 3, 4, 3, 4, 5, 4, 2, 2, 2, 3, 5, 5, 5, 5, 3, 2, 3, 2, 3, 3, 3
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OFFSET
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1,5
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LINKS
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FORMULA
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EXAMPLE
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For n=14: binomial(28,14) = 40116600 = 2*2*2*3*3*3*5*5*17*19*23;
unitary prime divisors: {17,19,23};
non-unitary prime divisors: {2,3,5}, so a(14)=3.
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MATHEMATICA
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Table[Count[Transpose[FactorInteger[Binomial[2n, n]]][[2]], _?(#>1&)], {n, 110}] (* Harvey P. Dale, Oct 08 2012 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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