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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
OFFSET
0,3
COMMENTS
A set is product-free if it contains no product of two (not necessarily distinct) elements.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..167, (terms up to a(100) from Andrew Howroyd)
Marcel K. Goh and Jonah Saks, Alternating-sum statistics for certain sets of integers, arXiv:2206.12535 [math.CO], 2022.
Andrew Howroyd, PARI Program
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.
Sequence in context: A370648 A326114 A135231 * A217356 A030793 A085988
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 09 2019
EXTENSIONS
a(21)-a(36) from Andrew Howroyd, Aug 25 2019
a(0)=1 prepended to data, example and b-file by Peter Kagey, Sep 18 2019
STATUS
approved