This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A090621 #12 Jul 10 2022 16:10:57 %S A090621 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 A090621 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 A090621 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 A090621 Exponent of highest power of 16 dividing n!. %F A090621 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 A090621 a(10)=2 since 10! = 3628800 = 16^2 * 14175. %o A090621 (Python 3.10+) %o A090621 def A090621(n): return (n-n.bit_count())>>2 # _Chai Wah Wu_, Jul 09 2022 %o A090621 (PARI) a(n) = valuation(n!, 16); \\ _Michel Marcus_, Jul 10 2022 %Y A090621 Cf. A011371, A054861, A090616, A027868, A054896, A090617, A090618, A090619, A090620. %K A090621 nonn %O A090621 0,11 %A A090621 _Henry Bottomley_, Dec 06 2003