login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 A143251

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 25 20:04 EST 2020. Contains 332258 sequences. (Running on oeis4.)