|
Search: id:A064277
|
|
|
| A064277 |
|
Anti-divisorial 2-decomposition values. |
|
+0
2
|
|
| 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; listen)
|
|
|
OFFSET
|
2,4
|
|
|
COMMENT
|
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: A075015 A082494 A110663 this_sequence A141155 A057669 A126136
Adjacent sequences: A064274 A064275 A064276 this_sequence A064278 A064279 A064280
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Jon Perry (perry(AT)globalnet.co.uk), Sep 24 2001
|
|
|
Search completed in 0.002 seconds
|
