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A302915
Number of relatively prime enriched p-trees of weight n.
4
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
OFFSET
1,2
COMMENTS
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.
EXAMPLE
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).
MATHEMATICA
a[n_]:=a[n]=1+Sum[Times@@a/@y, {y, Rest[Select[IntegerPartitions[n], Or[Length[#]===1, GCD@@#===1]&]]}];
Array[a, 20]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 15 2018
STATUS
approved