A240672 Number of the first evil exponents (A001969) in the prime power factorization of (2n)!.

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

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