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A213609
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Smallest number k such that the number of distinct prime divisors of binomial(2k,k) equals n, otherwise 0.
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1
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1, 2, 4, 6, 8, 11, 15, 16, 18, 20, 0, 28, 29, 33, 38, 42, 45, 48, 53, 54, 60, 64, 66, 67, 75, 77, 80, 86, 91, 92, 100, 102, 104, 109, 111, 110, 127, 0, 128, 133, 140, 144, 151, 154, 153, 160, 165, 170, 171, 178, 0, 189, 190, 192, 198, 202, 209, 210, 220, 225
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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a(3) = 4 because binomial(2*4,4) = 70 with 3 distinct prime divisors {2, 5, 7}.
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MAPLE
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with(numtheory): for n from 1 to 100 do:ii:=0: for k from 1 to 500 while(ii=0) do:x:=binomial(2*k, k):y:=factorset(x): n1:=nops(y):if n1=n then ii:=1:printf(`%d, `, k):else fi:od:if ii=0 then printf(`%d, `, 0):else fi:od:
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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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