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 A240668 Number of the first odd exponents in the prime power factorization of (2*n)!. 16
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS According to Chen's theorem, the sequence is unbounded. LINKS 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. FORMULA a(n)*A240606(n) = 0. EXAMPLE 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. MATHEMATICA Map[Count[First[Split[Mod[Last[Transpose[FactorInteger[(2*#)!]]], 2]]], 1]&, Range[75]] (* Peter J. C. Moses, Apr 10 2014 *) PROG (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 CROSSREFS Cf. A240537, A240606, A240619, A240620. Sequence in context: A025895 A104451 A285680 * A106602 A106594 A341026 Adjacent sequences:  A240665 A240666 A240667 * A240669 A240670 A240671 KEYWORD nonn AUTHOR Vladimir Shevelev, Apr 10 2014 EXTENSIONS More terms from Michel Marcus, Apr 10 2014 STATUS approved

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Last modified April 23 05:18 EDT 2021. Contains 343199 sequences. (Running on oeis4.)