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A082908
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Largest value of gcd(2^n, binomial(n,j)) with j=0..n-1; maximal value of largest power of 2 dividing binomial(n,j) in the n-th row of Pascal's triangle.
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1
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1, 1, 2, 1, 4, 2, 4, 1, 8, 4, 8, 2, 8, 4, 8, 1, 16, 8, 16, 4, 16, 8, 16, 2, 16, 8, 16, 4, 16, 8, 16, 1, 32, 16, 32, 8, 32, 16, 32, 4, 32, 16, 32, 8, 32, 16, 32, 2, 32, 16, 32, 8, 32, 16, 32, 4, 32, 16, 32, 8, 32, 16, 32, 1, 64, 32, 64, 16, 64, 32, 64, 8, 64, 32, 64, 16, 64, 32, 64, 4, 64, 32
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Max_{gcd(2^n, binomial(n, j)), j=0..n}.
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EXAMPLE
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n=10: 10th row = {1,10,45,120,210,252,210,120,45,10,1}, largest powers of 2 dividing entries: {1,2,1,8,2,4,2,8,1,2,1}; maximal 2^k-divisor is a(10)=8.
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MATHEMATICA
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Table[Max[Table[GCD[2^n, Binomial[n, j]], {j, 0, n}]], {n, 0, 128}]
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PROG
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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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