

A064277


Antidivisorial 2decomposition 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

Antidivisors are the numbers that do not divide a number with the largest possible margin. E.g. 20 has antidivisors 3, 8 and 13. An alternative name is unbiased nondivisors. These numbers have special significance because 5 is an antiperfect number, having antidivisors of 2 and 3. The 2decomposition technique involves continually finding the antidivisors of the antidivisors of a number, thus:
See A066272 for definition of antidivisor.


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 antidivisorial 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 2decomposition 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



