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A196722
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Number of subsets of {1..n} (including empty set) such that the pairwise LCMs of elements are not distinct.
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6
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1, 2, 4, 7, 11, 16, 23, 30, 38, 47, 58, 69, 83, 96, 111, 128, 144, 161, 181, 200, 223, 246, 269, 292, 319, 344, 371, 398, 429, 458, 496, 527, 559, 594, 629, 668, 708, 745, 784, 825, 870, 911, 962, 1005, 1052, 1102, 1149, 1196, 1248, 1297, 1349, 1402, 1457, 1510
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OFFSET
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0,2
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COMMENTS
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All pairwise LCMs of each subset are equal if there are any.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1000
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EXAMPLE
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A(6) = 23: {}, {1}, {2}, {3}, {4}, {5}, {6}, {1,2}, {1,3}, {1,4}, {1,5}, {1,6}, {2,3}, {2,4}, {2,5}, {2,6}, {3,4}, {3,5}, {3,6}, {4,5}, {4,6}, {5,6}, {2,3,6}.
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MAPLE
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b:= proc(n, s) local sn, m;
m:= nops(s);
sn:= [s[], n];
`if`(n<1, 1, b(n-1, s) +`if` (1 >= nops (({seq (seq (
ilcm (sn[i], sn[j]), j=i+1..m+1), i=1..m)})), b(n-1, sn), 0))
end:
a:= proc(n) option remember;
b(n-1, [n]) +`if` (n=0, 0, a(n-1))
end:
seq (a(n), n=0..50);
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CROSSREFS
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Cf. A143823, A196719, A196720, A196721, A196723, A196724.
Sequence in context: A131075 A133523 A114805 * A181120 A000601 A062433
Adjacent sequences: A196719 A196720 A196721 * A196723 A196724 A196725
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Oct 05 2011
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STATUS
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approved
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