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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 27 04:33 EDT 2022. Contains 357052 sequences. (Running on oeis4.)