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A302915
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Number of relatively prime enriched p-trees of weight n.
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4
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1, 2, 4, 8, 28, 56, 256, 656, 2480, 6688, 30736, 73984, 366560, 1006720, 3966976, 12738560, 58427648, 148069632, 764473600, 2133585664, 8939502080, 28705390592, 136987259648, 356634376704, 1780025034240, 5455065263104, 23215437079552, 73123382895616
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OFFSET
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1,2
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COMMENTS
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A relatively prime enriched p-tree of weight n is either a single node of weight n, or a finite sequence of two or more relatively prime enriched p-trees whose weights are weakly decreasing, relatively prime, and sum to n.
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LINKS
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EXAMPLE
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The a(4) = 8 relatively prime enriched p-trees are 4, (31), ((21)1), (((11)1)1), ((111)1), (211), ((11)11), (1111). Missing from this list are the enriched p-trees ((11)(11)), ((11)2), (2(11)), (22).
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MATHEMATICA
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a[n_]:=a[n]=1+Sum[Times@@a/@y, {y, Rest[Select[IntegerPartitions[n], Or[Length[#]===1, GCD@@#===1]&]]}];
Array[a, 20]
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CROSSREFS
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Cf. A000081, A000837, A003238, A004111, A055277, A093637, A196545, A289501, A290689, A300486, A301462, A301467, A302094, A302916, A302917.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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