A090329 - OEIS

%I #4 Mar 30 2012 18:50:42

%S 0,1,1,2,1,2,1,3,1,3,1,4,1,2,2,4,1,4,1,4,2,3,1,6,1,2,2,4,1,5,1,5,1,3,

%T 1,7,1,3,2,6,1,5,1,4,3,3,1,8,1,4,2,4,1,6,2,6,2,2,1,8,1,2,3,6,1,5,1,5,

%U 1,5,1,9,1,3,2,5,1,6,1,8,2,3,1,8,2,3,2,6,1,7,1,4,2,3,2,10,1,3,2,6,1,6

%N Number of divisors of n that are prefixes of other divisors of n in binary representation.

%C a(p) = 1 for all primes p;

%C a(n) = A090330(n) + 1.

%e Divisors of n=35: {1,5,7,35}, in binary {1,101,111,100011}: as

%e only '1' is a prefex, a(35)=1;

%e divisors of n=45: {1,3,5,9,15,45}, in binary

%e {1,11,101,1001,1111,101101}: '1' is a prefex of all other divisors, '11' of

%e '1111' and '101' of '101101', therefore a(45)=3.

%Y Cf. A000005.

%K nonn

%O 1,4

%A _Reinhard Zumkeller_, Nov 26 2003