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 A226590 #29 Apr 24 2022 06:36:03
%S A226590 0,1,0,3,1,2,0,6,2,4,1,6,1,2,1,10,3,7,2,9,2,4,1,12,3,4,3,6,1,6,0,15,5,
%T A226590 8,4,15,3,6,3,16,3,8,2,9,5,4,1,20,3,9,5,9,2,10,3,12,4,4,1,15,1,2,4,21,
%U A226590 7,14,4,15,5,12,3,26,4,8,6,12,4,10,2,25,7
%N A226590 Total number of 0's in binary expansion of all divisors of n.
%C A226590 Also total number of 0's in binary expansion of concatenation of the binary numbers that are the divisors of n written in base 2 (A182621).
%C A226590 a(n) = 0 iff n = 1 or n is a Mersenne prime (A000668). - _Bernard Schott_, Apr 22 2022
%H A226590 Jaroslav Krizek, <a href="/A226590/b226590.txt">Table of n, a(n) for n = 1..500</a>
%F A226590 a(n) = A182627(n) - A093653(n).
%F A226590 a(2^n) = n*(n+1)/2 = A000217(n). - _Bernard Schott_, Apr 22 2022
%e A226590 a(8) = 6 because the divisors of 8 are [1, 2, 4, 8] and in binary: 1, 10, 100, 1000, so six 0's.
%t A226590 Table[Count[Flatten[IntegerDigits[Divisors[n], 2]], 0], {n, 81}] (* _T. D. Noe_, Sep 04 2013 *)
%o A226590 (Python)
%o A226590 from sympy import divisors
%o A226590 def a(n): return sum(bin(d)[2:].count("0") for d in divisors(n))
%o A226590 print([a(n) for n in range(1, 88)]) # _Michael S. Branicky_, Apr 20 2022
%o A226590 (PARI) a(n) = sumdiv(n, d, 1+logint(d, 2) - hammingweight(d)); \\ _Michel Marcus_, Apr 24 2022
%Y A226590 Cf. A093653 (number of 1's in binary expansion of all divisors of n).
%Y A226590 Cf. A182627 (number of digits in binary expansion of all divisors of n).
%Y A226590 Cf. A182621 (concatenation of the divisors of n written in base 2).
%Y A226590 Cf. A000217, A000668.
%K A226590 base,nonn
%O A226590 1,4
%A A226590 _Jaroslav Krizek_, Aug 31 2013