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%I #5 Apr 16 2018 18:56:30
%S 1,2,4,8,28,56,256,656,2480,6688,30736,73984,366560,1006720,3966976,
%T 12738560,58427648,148069632,764473600,2133585664,8939502080,
%U 28705390592,136987259648,356634376704,1780025034240,5455065263104,23215437079552,73123382895616
%N Number of relatively prime enriched p-trees of weight n.
%C 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.
%e 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).
%t a[n_]:=a[n]=1+Sum[Times@@a/@y,{y,Rest[Select[IntegerPartitions[n],Or[Length[#]===1,GCD@@#===1]&]]}];
%t Array[a,20]
%Y Cf. A000081, A000837, A003238, A004111, A055277, A093637, A196545, A289501, A290689, A300486, A301462, A301467, A302094, A302916, A302917.
%K nonn
%O 1,2
%A _Gus Wiseman_, Apr 15 2018
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