A302915 Number of relatively prime enriched p-trees of weight n.

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.

Links

Table of n, a(n) for n=1..28.

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]

Crossrefs

Cf. A000081, A000837, A003238, A004111, A055277, A093637, A196545, A289501, A290689, A300486, A301462, A301467, A302094, A302916, A302917.

Sequence in context: A326293 A324328 A056800 * A259135 A219969 A034919

Adjacent sequences: A302912 A302913 A302914 * A302916 A302917 A302918

Keyword

nonn

Author

Gus Wiseman, Apr 15 2018

Status

approved