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 A079584 #44 Mar 07 2023 20:11:02
%S A079584 1,1,1,2,2,4,4,6,6,6,11,7,12,12,12,18,18,22,23,17,22,25,28,31,29,30,
%T A079584 35,38,42,40,48,42,42,46,51,56,51,58,59,64,63,66,64,71,74,70,77,81,89,
%U A079584 87,89,90,88,94,87,99,103,98,101,109,113,103,113,120,120,109,123,121,130,121
%N A079584 Number of ones in the binary expansion of n!.
%H A079584 Charles R Greathouse IV, <a href="/A079584/b079584.txt">Table of n, a(n) for n = 0..10000</a>
%H A079584 Florian Luca, <a href="http://dx.doi.org/10.4153/CMB-2002-013-9">The number of non-zero digits of n!</a>, Canad. Math. Bull. 45 (2002), pp. 115-118.
%H A079584 Carlo Sanna, <a href="http://arxiv.org/abs/1409.4912">On the sum of digits of the factorial</a>, arXiv:1409.4912 [math.NT], 2014.
%H A079584 Carlo Sanna, <a href="http://dx.doi.org/10.1016/j.jnt.2014.09.003">On the sum of digits of the factorial</a>, Journal of Number Theory 147 (2015), pp. 836-841.
%H A079584 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A079584 a(n) << n log n. - _Charles R Greathouse IV_, Mar 27 2013
%F A079584 a(n) = A000120(A000142(n)). - _Michel Marcus_, Sep 18 2014
%e A079584 a(5) = 4 because 5! = 120 and 120_10 = 1111000_2, with 4 ones.
%p A079584 seq(convert(convert(n!,base,2),`+`), n=0..1000); # _Robert Israel_, Sep 18 2014
%t A079584 Table[DigitCount[n!,2,1],{n,70}] (* _Harvey P. Dale_, Jul 10 2012 *)
%o A079584 (PARI) for(n=1,300,b=binary(n!); print1(sum(k=1,length(b),b[k])","))
%o A079584 (PARI) a(n)=hammingweight(n!) \\ _Charles R Greathouse IV_, Mar 27 2013
%o A079584 (Python)
%o A079584 import math
%o A079584 def a(n):
%o A079584 return bin(math.factorial(n))[2:].count("1") # _Indranil Ghosh_, Dec 23 2016
%Y A079584 Cf. A000120 (binary weight), A000142 (factorial), A004152 (sum of decimal digits).
%K A079584 nonn,base
%O A079584 0,4
%A A079584 Jose R. Brox (tautocrona(AT)terra.es), Jan 26 2003
%E A079584 a(0)=1 prepended by _Alois P. Heinz_, Mar 07 2023