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A240668
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Number of the first odd exponents in the prime power factorization of (2*n)!.
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16
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1, 2, 0, 1, 0, 0, 2, 1, 0, 0, 2, 0, 1, 2, 0, 1, 0, 0, 2, 0, 3, 3, 0, 0, 1, 2, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 5, 0, 1, 0, 0, 3, 0, 1, 1, 0, 2, 0, 0, 2, 1, 0, 0, 3, 0, 1, 2, 0, 3, 0, 0, 2, 0, 5, 2, 0, 0, 1, 3, 0, 1, 0, 0, 2, 0, 1, 1, 0, 1, 0, 0, 4
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OFFSET
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1,2
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COMMENTS
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According to Chen's theorem, the sequence is unbounded.
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LINKS
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Peter J. C. Moses, Table of n, a(n) for n = 1..10000
D. Berend, Parity of exponents in the factorization of n!, J. Number Theory, 64 (1997), 13-19.
Y.-G. Chen, On the parity of exponents in the standard factorization of n!, J. Number Theory, 100 (2003), 326-331.
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FORMULA
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a(n)*A240606(n) = 0.
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EXAMPLE
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32! = 2^31*3^14*5^7*7^4*11^2*13^2*17*19*23*29*31, and only the first 1 exponent is odd, so a(16) = 1.
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MATHEMATICA
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Map[Count[First[Split[Mod[Last[Transpose[FactorInteger[(2*#)!]]], 2]]], 1]&, Range[75]] (* Peter J. C. Moses, Apr 10 2014 *)
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PROG
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(PARI) a(n) = {my(f = factor((2*n)!)); my(nb = 0); my(i = 1); while((i <= #f~) && (f[i, 2] % 2), nb++; i++; ); nb; } \\ Michel Marcus, Apr 10 2014
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CROSSREFS
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Cf. A240537, A240606, A240619, A240620.
Sequence in context: A025895 A104451 A285680 * A106602 A106594 A341026
Adjacent sequences: A240665 A240666 A240667 * A240669 A240670 A240671
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KEYWORD
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nonn
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AUTHOR
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Vladimir Shevelev, Apr 10 2014
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EXTENSIONS
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More terms from Michel Marcus, Apr 10 2014
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STATUS
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approved
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