2,4

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:

See A066272 for definition of anti-divisor.

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.

20:

3.8.13:

2. 3.5. 2.3.5.9:

2. 2.2.3. 2.2.2.3.2.6:

2. 2.2.2. 2.2.2.2.2.4:

2. 2.2.2. 2.2.2.2.2.3:

2. 2.2.2. 2.2.2.2.2.2

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

Sequence in context: A075015 A082494 A110663 this_sequence A144330 A141155 A057669

Adjacent sequences: A064274 A064275 A064276 this_sequence A064278 A064279 A064280

nonn

Jon Perry (perry(AT)globalnet.co.uk), Sep 24 2001