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%I #12 Aug 11 2014 22:46:11
%S 0,1,0,0,0,2,0,3,0,1,0,0,4,0,0,0,0,2,0,0,1,0,0,1,0,0,0,1,2,0,1,2,0,1,
%T 0,0,2,0,0,2,0,0,0,1,1,0,2,0,2,0,0,1,1,0,2,0,0,0,9,2,0,1,1,0,0,2,0,0,
%U 1,0,0,1,0,0,0,2,1,0,2,0,3,0,0,1,1,0,2
%N Number of the first evil exponents (A001969) in the prime power factorization of (2n)!.
%C Conjecture: The sequence is unbounded. (This conjecture does not follow from Chen's theorem.)
%H Peter J. C. Moses, <a href="/A240672/b240672.txt">Table of n, a(n) for n = 1..2000</a>
%H Y.-G. Chen, <a href="http://dx.doi.org/10.1016/S0022-314X(03)00013-1">On the parity of exponents in the standard factorization of n!</a>, J. Number Theory, 100 (2003), 326-331.
%F a(n)*A240669(n) = 0.
%e 26! = 2^23*3^10*5^6*7^3*11^2*13^2*17*19*23, and the first 4 exponents (23,10,6,3) are evil, so a(13) = 4.
%t Map[Count[First[Split[Map[EvenQ[DigitCount[#,2][[1]]]&,Last[Transpose[FactorInteger[(2*#)!]]&[#]]]]],True]&,Range[75]] (* _Peter J. C. Moses_, Apr 10 2014 *)
%Y Cf. A001969, A240537, A240606, A240619, A240620, A240668, A240669, A240670.
%K nonn
%O 1,6
%A _Vladimir Shevelev_, Apr 10 2014
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