|
|
A326489
|
|
Number of product-free subsets of {1..n}.
|
|
12
|
|
|
1, 1, 2, 4, 6, 12, 22, 44, 88, 136, 252, 504, 896, 1792, 3392, 6352, 9720, 19440, 35664, 71328, 129952, 247232, 477664, 955328, 1700416, 2657280, 5184000, 10368000, 19407360, 38814720, 68868352, 137736704, 260693504, 505830400, 999641600, 1882820608, 2807196672
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
A set is product-free if it contains no product of two (not necessarily distinct) elements.
|
|
LINKS
|
|
|
EXAMPLE
|
The a(0) = 1 through a(6) = 22 subsets:
{} {} {} {} {} {} {}
{2} {2} {2} {2} {2}
{3} {3} {3} {3}
{2,3} {4} {4} {4}
{2,3} {5} {5}
{3,4} {2,3} {6}
{2,5} {2,3}
{3,4} {2,5}
{3,5} {2,6}
{4,5} {3,4}
{2,3,5} {3,5}
{3,4,5} {3,6}
{4,5}
{4,6}
{5,6}
{2,3,5}
{2,5,6}
{3,4,5}
{3,4,6}
{3,5,6}
{4,5,6}
{3,4,5,6}
|
|
MATHEMATICA
|
Table[Length[Select[Subsets[Range[n]], Intersection[#, Times@@@Tuples[#, 2]]=={}&]], {n, 10}]
|
|
CROSSREFS
|
Product-closed subsets are A326076.
Subsets containing no products are A326114.
Subsets containing no products of distinct elements are A326117.
Subsets containing no quotients are A327591.
Maximal product-free subsets are A326496.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
a(0)=1 prepended to data, example and b-file by Peter Kagey, Sep 18 2019
|
|
STATUS
|
approved
|
|
|
|