A090617 - OEIS

%I #16 Jul 10 2022 16:10:41

%S 0,0,0,0,1,1,1,1,2,2,2,2,3,3,3,3,5,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,10,

%T 10,10,10,11,11,11,11,12,12,13,13,13,13,14,14,15,15,15,15,16,16,16,16,

%U 17,17,18,18,18,18,19,19,21,21,21,21,22,22,22,22,23,23,23,23,24,24,24,24

%N Exponent of highest power of 8 dividing n!.

%F a(n) = A090622(n, 8) = floor(A011371(n)/3) = floor((floor(n/2) + floor(n/4) + floor(n/8) + floor(n/16) + ...)/3).

%F a(n) = A244413(n!) . - _R. J. Mathar_, Jul 08 2021

%e a(8)=2 since 8! = 40320 = 8^2 * 630.

%t Table[IntegerExponent[n!,8],{n,0,80}] (* _Harvey P. Dale_, Mar 21 2013 *)

%o (Python 3.10+)

%o def A090617(n): return (n-bin(n).count('1'))//3 # _Chai Wah Wu_, Jul 09 2022

%o (PARI) a(n) = valuation(n!, 8); \\ _Michel Marcus_, Jul 10 2022

%Y Cf. A011371, A054861, A090616, A027868, A054896.

%K nonn

%O 0,9

%A _Henry Bottomley_, Dec 06 2003