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A064277
Anti-divisorial 2-decomposition values.
1
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
2,4
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.
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.
EXAMPLE
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.
CROSSREFS
Sequence in context: A174375 A110663 A294317 * A287010 A144330 A141155
KEYWORD
nonn
AUTHOR
Jon Perry, Sep 24 2001
STATUS
approved