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%I #40 Jun 27 2022 23:34:34
%S 1,1,2,4,6,12,22,44,88,136,252,504,896,1792,3392,6352,9720,19440,
%T 35664,71328,129952,247232,477664,955328,1700416,2657280,5184000,
%U 10368000,19407360,38814720,68868352,137736704,260693504,505830400,999641600,1882820608,2807196672
%N Number of product-free subsets of {1..n}.
%C A set is product-free if it contains no product of two (not necessarily distinct) elements.
%H Fausto A. C. Cariboni, <a href="/A326489/b326489.txt">Table of n, a(n) for n = 0..167</a>, (terms up to a(100) from Andrew Howroyd)
%H Marcel K. Goh and Jonah Saks, <a href="https://arxiv.org/abs/2206.12535">Alternating-sum statistics for certain sets of integers</a>, arXiv:2206.12535 [math.CO], 2022.
%H Andrew Howroyd, <a href="/A326489/a326489.txt">PARI Program</a>
%e The a(0) = 1 through a(6) = 22 subsets:
%e {} {} {} {} {} {} {}
%e {2} {2} {2} {2} {2}
%e {3} {3} {3} {3}
%e {2,3} {4} {4} {4}
%e {2,3} {5} {5}
%e {3,4} {2,3} {6}
%e {2,5} {2,3}
%e {3,4} {2,5}
%e {3,5} {2,6}
%e {4,5} {3,4}
%e {2,3,5} {3,5}
%e {3,4,5} {3,6}
%e {4,5}
%e {4,6}
%e {5,6}
%e {2,3,5}
%e {2,5,6}
%e {3,4,5}
%e {3,4,6}
%e {3,5,6}
%e {4,5,6}
%e {3,4,5,6}
%t Table[Length[Select[Subsets[Range[n]],Intersection[#,Times@@@Tuples[#,2]]=={}&]],{n,10}]
%Y Product-closed subsets are A326076.
%Y Subsets containing no products are A326114.
%Y Subsets containing no products of distinct elements are A326117.
%Y Subsets containing no quotients are A327591.
%Y Maximal product-free subsets are A326496.
%Y Cf. A007865, A051026, A326023, A326081, A326116, A326495.
%K nonn
%O 0,3
%A _Gus Wiseman_, Jul 09 2019
%E a(21)-a(36) from _Andrew Howroyd_, Aug 25 2019
%E a(0)=1 prepended to data, example and b-file by _Peter Kagey_, Sep 18 2019
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