%I #6 Mar 31 2012 13:21:54

%S 1,1,1,2,1,4,3,2,6,6,5,6,4,8,7,14,12,8,10,6,14,14,11,26,16,22,20,10,

%T 16,14,21,24,16,26,14,38,48,28,32,26,42,28,14,46,26,26,31,38,44,18,50,

%U 48,20,60,46,66,54,56,70,34,56,88,29,52,32,94,84,28,58,40,62,62,50,68,38

%N Anti-divisorial 2-decomposition values.

%C Anti-divisors are the numbers that do not divide a number with the largest possible margin. E.g. 20 has anti-divisors 3, 8 and 13. An alternative name is unbiased non-divisors. These numbers have special significance because 5 is an anti-perfect number, having anti-divisors of 2 and 3. The 2-decomposition technique involves continually finding the anti-divisors of the anti-divisors of a number, thus:

%C See A066272 for definition of anti-divisor.

%F The number of 2's is the sum of the number of 2's in the primary anti-divisorial decomposition, e.g. 20 has d(3) + d(8) + d(13) 2's by the final decomposition.

%e 20:

%e 3.8.13:

%e 2. 3.5. 2.3.5.9:

%e 2. 2.2.3. 2.2.2.3.2.6:

%e 2. 2.2.2. 2.2.2.2.2.4:

%e 2. 2.2.2. 2.2.2.2.2.3:

%e 2. 2.2.2. 2.2.2.2.2.2

%e Therefore the value of the 2-decomposition of 20 is 10.

%K nonn

%O 2,4

%A _Jon Perry_, Sep 24 2001