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A298676
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Number of partitions of n that can be uniquely recovered from their P-graphs.
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0
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1, 2, 3, 5, 5, 7, 7, 10, 11, 13, 13, 18, 19, 26, 31, 36, 41, 48, 59, 71, 84, 94, 106, 123, 146, 165, 187, 210, 240, 275, 318, 364, 407, 465, 525, 593, 672, 756, 849, 966, 1080, 1207, 1354, 1530, 1718, 1925, 2135, 2377, 2667, 2997, 3351, 3736, 4141, 4598, 5125
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OFFSET
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1,2
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COMMENTS
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a(n) is the number of partitions of n that can be uniquely recovered from its P-graph, the simple graph whose vertices are the parts of the partition, two of which are joined by an edge if, and only if, they have a common factor greater than 1.
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LINKS
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EXAMPLE
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a(1) = 1 because the sole partition of 1 can be recovered from its P-graph, a single vertex.
a(2) = 2 because both partitions of 2 can be recovered from their corresponding P-graphs.
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MATHEMATICA
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pgraph[p_] := With[{v = Range[Length[p]]}, Graph[v, UndirectedEdge @@@ Select[Subsets[v, {2}], !CoprimeQ @@ p[[#]] &]]];
a[n_] := Count[Length /@ Gather[pgraph /@ IntegerPartitions[n], IsomorphicGraphQ], 1];
Array[a, 20]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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