A240669 Number of the first odious exponents (A000069) in the prime power factorization of (2n)!.

1, 0, 3, 4, 4, 0, 1, 0, 2, 0, 1, 1, 0, 2, 10, 11, 1, 0, 1, 1, 0, 2, 2, 0, 2, 1, 2, 0, 0, 3, 0, 0, 2, 0, 4, 1, 0, 2, 1, 0, 1, 5, 2, 0, 0, 6, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 3, 2, 0, 0, 1, 0, 0, 3, 3, 0, 1, 1, 0, 2, 1, 0, 8, 1, 1, 0, 0, 1, 0, 2, 0, 1, 2, 0, 0, 3

Offset: 1

Author

Vladimir Shevelev, Apr 10 2014

Keywords

• nonn

Comments

Conjecture: The sequence is unbounded. (This conjecture does not follow from Chen's theorem.)

Examples

			28! = 2^25*3^13*5^6*7^4*11^2*13^2*17*19*23, and only the first 2 exponents are odious, so a(14) = 2.
		

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.

Crossrefs

Cf. A000069, A240537, A240606, A240619, A240620, A240668.

Programs

Mathematica

Map[Count[First[Split[Map[OddQ[DigitCount[#,2][[1]]]&,Last[Transpose[FactorInteger[(2*#)!]]&[#]]]]],True]&,Range[75]] (* Peter J. C. Moses, Apr 10 2014 *)