A064277 Anti-divisorial 2-decomposition values.

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, 16, 14, 21, 24, 16, 26, 14, 38, 48, 28, 32, 26, 42, 28, 14, 46, 26, 26, 31, 38, 44, 18, 50, 48, 20, 60, 46, 66, 54, 56, 70, 34, 56, 88, 29, 52, 32, 94, 84, 28, 58, 40, 62, 62, 50, 68, 38

Offset: 2

Author

Jon Perry, Sep 24 2001

Keywords

• nonn

Comments

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.

Examples

			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.
		

Formula

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.