A090621 - OEIS

%I #13 Sep 29 2025 23:26:57

%S 0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,3,3,4,4,4,4,4,4,5,5,5,5,6,6,6,6,7,7,

%T 8,8,8,8,8,8,9,9,9,9,10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,

%U 14,14,14,14,15,15,16,16,16,16,16,16,17,17,17,17,18,18,18,18,19,19,19,19

%N Exponent of highest power of 16 dividing n!.

%F a(n) = A090622(n, 16) = floor(A011371(n)/4) = floor(A090616(n)/2) = floor((floor(n/2) + floor(n/4) + floor(n/8) + floor(n/16) + ...)/4). Almost n/4.

%e a(10)=2 since 10! = 3628800 = 16^2 * 14175.

%o (Python)

%o def A090621(n): return (n-n.bit_count())>>2 # _Chai Wah Wu_, Jul 09 2022

%o (PARI) a(n) = valuation(n!, 16); \\ _Michel Marcus_, Jul 10 2022

%Y Cf. A011371, A054861, A090616, A027868, A054896, A090617, A090618, A090619, A090620.

%K nonn

%O 0,11

%A _Henry Bottomley_, Dec 06 2003