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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=2..76.

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

Adjacent sequences:  A064274 A064275 A064276 * A064278 A064279 A064280

KEYWORD

nonn

AUTHOR

Jon Perry, Sep 24 2001

STATUS

approved

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Last modified April 5 20:58 EDT 2020. Contains 333260 sequences. (Running on oeis4.)