A090616 - OEIS

%I #22 Jul 10 2022 16:10:27

%S 0,0,0,0,1,1,2,2,3,3,4,4,5,5,5,5,7,7,8,8,9,9,9,9,11,11,11,11,12,12,13,

%T 13,15,15,16,16,17,17,17,17,19,19,19,19,20,20,21,21,23,23,23,23,24,24,

%U 25,25,26,26,27,27,28,28,28,28,31,31,32,32,33,33,33,33,35,35,35,35,36

%N Exponent of highest power of 4 dividing n!.

%H Vincenzo Librandi, <a href="/A090616/b090616.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A090622(n, 4) = floor(A011371(n)/2) = floor((floor(n/2) + floor(n/4) + floor(n/8) + floor(n/16) + ...)/2).

%F a(n) = A235127(n!). - _R. J. Mathar_, Jul 08 2021

%e a(6)=2 since 6! = 720 = 4^2 * 45.

%t IntegerExponent[Range[0, 100]!, 4] (* _Vincenzo Librandi_, Mar 10 2013 *)

%o (PARI) a(n) = valuation( n!, 4 ); /* _Joerg Arndt_, Mar 10 2013 */

%o (Python 3.10+)

%o def A090616(n): return (n-n.bit_count())>>1 # _Chai Wah Wu_, Jul 09 2022

%Y Cf. A011371, A054861, A027868, A054896, A235127.

%K nonn

%O 0,7

%A _Henry Bottomley_, Dec 06 2003