cp's OEIS Frontend

A071425 Total number of 1's in binary representation of all factorials from 1 to n.

%I A071425 #33 Mar 18 2025 07:30:20
%S A071425 1,2,4,6,10,14,20,26,32,43,50,62,74,86,104,122,144,167,184,206,231,
%T A071425 259,290,319,349,384,422,464,504,552,594,636,682,733,789,840,898,957,
%U A071425 1021,1084,1150,1214,1285,1359,1429,1506,1587,1676,1763,1852,1942,2030,2124
%N A071425 Total number of 1's in binary representation of all factorials from 1 to n.
%H A071425 Amiram Eldar, <a href="/A071425/b071425.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%F A071425 a(n) = Sum_{i=1..n} A079584(i).
%t A071425 s=0; Do[s=s+Apply[Plus, IntegerDigits[n!, 2]]; Print[s], {n, 1, 128}]
%t A071425 Accumulate[DigitCount[Range[60]!,2,1]] (* _Harvey P. Dale_, Apr 18 2014 *)
%o A071425 (Python)
%o A071425 def A071425(n):
%o A071425     c, a = 0, 1
%o A071425     for i in range(1,n+1):
%o A071425         c += (a:=a*i).bit_count()
%o A071425     return c # _Chai Wah Wu_, Nov 12 2024
%o A071425 (PARI) list(lim) = {my(s = 0); for(k = 1, lim, s += hammingweight(k!); print1(s, ", "));} \\ _Amiram Eldar_, Mar 18 2025
%Y A071425 Cf. A000142, A000788.
%Y A071425 Partial sums of A079584 starting at index 1.
%K A071425 base,easy,nonn
%O A071425 1,2
%A A071425 _Labos Elemer_, May 27 2002