cp's OEIS Frontend

A090616 Exponent of highest power of 4 dividing n!.

%I A090616 #22 Jul 10 2022 16:10:27
%S A090616 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 A090616 13,15,15,16,16,17,17,17,17,19,19,19,19,20,20,21,21,23,23,23,23,24,24,
%U A090616 25,25,26,26,27,27,28,28,28,28,31,31,32,32,33,33,33,33,35,35,35,35,36
%N A090616 Exponent of highest power of 4 dividing n!.
%H A090616 Vincenzo Librandi, <a href="/A090616/b090616.txt">Table of n, a(n) for n = 0..10000</a>
%F A090616 a(n) = A090622(n, 4) = floor(A011371(n)/2) = floor((floor(n/2) + floor(n/4) + floor(n/8) + floor(n/16) + ...)/2).
%F A090616 a(n) = A235127(n!). - _R. J. Mathar_, Jul 08 2021
%e A090616 a(6)=2 since 6! = 720 = 4^2 * 45.
%t A090616 IntegerExponent[Range[0, 100]!, 4] (* _Vincenzo Librandi_, Mar 10 2013 *)
%o A090616 (PARI) a(n) = valuation( n!, 4 ); /* _Joerg Arndt_, Mar 10 2013 */
%o A090616 (Python 3.10+)
%o A090616 def A090616(n): return (n-n.bit_count())>>1 # _Chai Wah Wu_, Jul 09 2022
%Y A090616 Cf. A011371, A054861, A027868, A054896, A235127.
%K A090616 nonn
%O A090616 0,7
%A A090616 _Henry Bottomley_, Dec 06 2003