%I #47 Apr 09 2023 16:57:55
%S 1,1,2,1,2,2,2,1,2,2,2,2,2,2,4,1,2,2,2,2,2,2,2,2,2,2,4,2,2,4,2,1,2,2,
%T 2,2,2,2,3,2,2,2,2,2,4,2,2,2,2,2,4,2,2,4,3,2,2,2,2,4,2,2,6,1,2,2,2,2,
%U 2,2,2,2,2,2,3,2,2,3,2,2,2,2,2,2,4,2,3,2,2,4,2
%N Number of divisors d of n with property that the binary representation of d can be obtained from the binary representation of n by changing any number of 1's to 0's.
%C Equivalently, the number of divisors d of n such that the bitwise OR of n and d is equal to n. - _Chai Wah Wu_, Sep 06 2014
%C Equivalently, the number of divisors d of n such that the bitwise AND of n and d is equal to d. - _Amiram Eldar_, Dec 15 2022
%C The sums of the first 10^k terms for k = 1, 2, ..., are 16, 224, 2580, 26920, 273407, 2745100, 27440305, 274127749, 2738936912, 27373288534, 273631055291, 2735755647065, ... . Conjecture: The asymptotic mean of this sequence is 1 + Sum_{k>=1} 1/(k*2^A000120(k)) = 2.7351180693... . - _Amiram Eldar_, Apr 07 2023
%H N. J. A. Sloane, <a href="/A246600/b246600.txt">Table of n, a(n) for n = 1..10000</a>
%F a(2^i) = 1.
%F a(odd prime) = 2.
%F a(n) <= 2^wt(n)-1, where wt(n) = A000120(n).
%F a(n) = Sum_{d|n} (binomial(n,d) mod 2). - _Ridouane Oudra_, May 03 2019
%F From _Amiram Eldar_, Dec 15 2022: (Start)
%F a(2*n) = a(n), and therefore a(m*2^k) = a(m) for m odd and k>=0.
%F a(2^n-1) = A000005(2^n-1) = A046801(n). (End)
%e 12 = 1100_2; only the divisors 4 = 0100_2 and 12 = 1100_2 satisfy the condition, so(12)=2.
%e 15 = 1111_2; all divisors 1,3,5,15 satisfy the condition, so a(15)=4.
%p A246600:=proc(n)
%p local a, d, s, t, i, sw;
%p a:=0;
%p s:=convert(n, base, 2);
%p for d in numtheory[divisors](n) do
%p sw:= false;
%p t:=convert(d, base, 2);
%p for i from 1 to nops(t) do
%p if t[i]>s[i] then
%p sw:= true;
%p fi;
%p od:
%p if not sw then
%p a:=a+1;
%p fi;
%p od;
%p a;
%p end;
%p seq(A246600(n), n=1..100);
%t a[n_] := DivisorSum[n, Boole[BitOr[#, n] == n]&]; Array[a, 100] (* _Jean-François Alcover_, Dec 02 2015, adapted from PARI *)
%o (Python)
%o from sympy import divisors
%o def A246600(n):
%o return sum(1 for d in divisors(n) if n|d == n)
%o # _Chai Wah Wu_, Sep 06 2014
%o (PARI) a(n)=sumdiv(n,d,bitor(d,n)==n) \\ _Charles R Greathouse IV_, Sep 29 2014
%Y Cf. A000005, A000120, A046801, A246601.
%K nonn,base
%O 1,3
%A _N. J. A. Sloane_, Sep 06 2014