A090329 Number of divisors of n that are prefixes of other divisors of n in binary representation.

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, 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, 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

Offset: 1

Author

Reinhard Zumkeller, Nov 26 2003

Keywords

• nonn
• base

Examples

			Divisors of n = 35: {1,5,7,35}, in binary {1,101,111,100011}: as only '1' is a prefix, a(35) = 1;
Divisors of n = 45: {1,3,5,9,15,45}, in binary {1,11,101,1001,1111,101101}: '1' is a prefix of all other divisors, '11' of '1111' and '101' of '101101', therefore a(45) = 3.
		

Crossrefs

Cf. A000005, A090330.

Formula

a(p) = 1 for all primes p.

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