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 A240672 Number of the first evil exponents (A001969) in the prime power factorization of (2n)!. 13
 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, 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, 1, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 0, 3, 0, 0, 1, 1, 0, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Conjecture: The sequence is unbounded. (This conjecture does not follow from Chen's theorem.) LINKS Peter J. C. Moses, Table of n, a(n) for n = 1..2000 Y.-G. Chen, On the parity of exponents in the standard factorization of n!, J. Number Theory, 100 (2003), 326-331. FORMULA a(n)*A240669(n) = 0. EXAMPLE 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. MATHEMATICA Map[Count[First[Split[Map[EvenQ[DigitCount[#, 2][[1]]]&, Last[Transpose[FactorInteger[(2*#)!]]&[#]]]]], True]&, Range[75]] (* Peter J. C. Moses, Apr 10 2014 *) CROSSREFS Cf. A001969, A240537, A240606, A240619, A240620, A240668, A240669, A240670. Sequence in context: A113290 A078442 A175663 * A352288 A243016 A284975 Adjacent sequences: A240669 A240670 A240671 * A240673 A240674 A240675 KEYWORD nonn AUTHOR Vladimir Shevelev, Apr 10 2014 STATUS approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)