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%I #12 Jul 10 2022 16:10:57
%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 3.10+)
%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
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