%I #25 Nov 13 2024 16:42:58
%S 1,2,4,6,10,14,20,26,32,43,50,62,74,86,104,122,144,167,184,206,231,
%T 259,290,319,349,384,422,464,504,552,594,636,682,733,789,840,898,957,
%U 1021,1084,1150,1214,1285,1359,1429,1506,1587,1676,1763,1852,1942,2030,2124
%N Total number of 1-s in binary representation of all factorials from 1 to n.
%H Harvey P. Dale, <a href="/A071425/b071425.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{i=1..n} A079584(i).
%t s=0; Do[s=s+Apply[Plus, IntegerDigits[n!, 2]]; Print[s], {n, 1, 128}]
%t Accumulate[DigitCount[Range[60]!,2,1]] (* _Harvey P. Dale_, Apr 18 2014 *)
%o (Python)
%o def A071425(n):
%o c, a = 0, 1
%o for i in range(1,n+1):
%o c += (a:=a*i).bit_count()
%o return c # _Chai Wah Wu_, Nov 12 2024
%Y Cf. A000142, A000788.
%Y Partial sums of A079584 starting at index 1.
%K base,easy,nonn,changed
%O 1,2
%A _Labos Elemer_, May 27 2002