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A281145 Number of same-trees of weight n.

%I A281145 #21 Aug 20 2018 20:50:52
%S A281145 1,2,2,6,2,14,2,54,10,38,2,494,2,134,42,4470,2,3422,2,10262,138,2054,
%T A281145 2,490926,34,8198,1514,314294,2,628318,2,30229110,2058,131078,162,
%U A281145 150147342,2,524294,8202,628073814,2,109952254,2,371210294,207370,8388614,2
%N A281145 Number of same-trees of weight n.
%C A281145 A same-tree is either: (case 1) a positive integer, or (case 2) a finite sequence of two or more same-trees all having the same weight, where the weight in case 2 is the sum of weights.
%H A281145 G. C. Greubel, <a href="/A281145/b281145.txt">Table of n, a(n) for n = 1..4000</a>
%F A281145 a(n) = 1 + Sum a(d)^(n/d) where the sum is over divisors less than n.
%e A281145 The a(6)=14 same-trees are:
%e A281145 6,
%e A281145 (33),
%e A281145 (222),
%e A281145 (3(111)), ((111)3),
%e A281145 (22(11)), (2(11)2), ((11)22),
%e A281145 (2(11)(11)), ((11)2(11)), ((11)(11)2),
%e A281145 ((111)(111)), ((11)(11)(11)), (111111).
%e A281145 The a(9)=10 same-trees are:
%e A281145 9,
%e A281145 (333),
%e A281145 (33(111)), (3(111)3), ((111)33),
%e A281145 (3(111)(111)), ((111)3(111)), ((111)(111)3),
%e A281145 ((111)(111)(111)), (111111111).
%t A281145 a[n_]:=1+DivisorSum[n,b[#]^(n/#)&]-b[n]/.b->a;
%t A281145 Array[a,47]
%o A281145 (PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n] = 1 + sumdiv(n, d, v[n/d]^d)); v} \\ _Andrew Howroyd_, Aug 20 2018
%Y A281145 Cf. A196545, A260685, A273873, A275870, A006241.
%K A281145 nonn
%O A281145 1,2
%A A281145 _Gus Wiseman_, Jan 15 2017