|
| |
|
|
A370586
|
|
Number of subsets of {1..n} containing n such that it is possible to choose a different prime factor of each element (choosable).
|
|
17
|
|
|
|
0, 0, 1, 2, 2, 6, 8, 20, 12, 20, 44, 116, 88, 320, 380, 508, 264, 1792, 968, 4552, 3136, 5600, 10056, 27896, 11792, 16384, 46688, 19584, 48288, 198528, 110928, 507984, 99648, 463552, 859376, 821136, 470688, 3730368, 4033920, 4651296, 2932512, 19078464
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,4
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
The a(0) = 0 through a(7) = 20 subsets:
. . {2} {3} {4} {5} {6} {7}
{2,3} {3,4} {2,5} {2,6} {2,7}
{3,5} {3,6} {3,7}
{4,5} {4,6} {4,7}
{2,3,5} {5,6} {5,7}
{3,4,5} {2,5,6} {6,7}
{3,5,6} {2,3,7}
{4,5,6} {2,5,7}
{2,6,7}
{3,4,7}
{3,5,7}
{3,6,7}
{4,5,7}
{4,6,7}
{5,6,7}
{2,3,5,7}
{2,5,6,7}
{3,4,5,7}
{3,5,6,7}
{4,5,6,7}
|
|
|
MATHEMATICA
|
Table[Length[Select[Subsets[Range[n]], MemberQ[#, n]&&Length[Select[Tuples[If[#==1, {}, First/@FactorInteger[#]]&/@#], UnsameQ@@#&]]>0&]], {n, 0, 10}]
|
|
|
CROSSREFS
|
Maximal choosable sets are counted by A370585.
The complement is counted by A370587.
For a unique choice we have A370588.
For binary indices instead of prime factors we have A370639.
A355741 counts choices of a prime factor of each prime index.
A368098 counts choosable unlabeled multiset partitions, complement A368097.
Cf. A000040, A000720, A005117, A045778, A133686, A355739, A355744, A355745, A367771, A367905, A370636.
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
