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A300647 Number of same-trees of weight n in which all outdegrees are odd.

%I A300647 #11 May 31 2021 17:46:29
%S A300647 1,1,2,1,2,2,2,1,10,2,2,2,2,2,42,1,2,10,2,2,138,2,2,2,34,2,1514,2,2,
%T A300647 42,2,1,2058,2,162,10,2,2,8202,2,2,138,2,2,207370,2,2,2,130,34,131082,
%U A300647 2,2,1514,2082,2,524298,2,2,42,2,2,14725738,1,8226,2058,2
%N A300647 Number of same-trees of weight n in which all outdegrees are odd.
%C A300647 A same-tree of weight n > 0 is either a single node of weight n, or a finite sequence of two or more same-trees whose weights are all equal and sum to n.
%H A300647 Antti Karttunen, <a href="/A300647/b300647.txt">Table of n, a(n) for n = 1..8192</a>
%F A300647 a(n) = 1 + Sum_d a(n/d)^d where the sum is over odd divisors of n greater than 1.
%e A300647 The a(9) = 10 odd same-trees:
%e A300647 9,
%e A300647 (333),
%e A300647 (33(111)), (3(111)3), ((111)33)
%e A300647 (3(111)(111)), ((111)3(111)), ((111)(111)3),
%e A300647 ((111)(111)(111)), (111111111).
%t A300647 a[n_]:=1+Sum[a[n/d]^d,{d,Select[Rest[Divisors[n]],OddQ]}];
%t A300647 Array[a,80]
%o A300647 (PARI) a(n) = if (n==1, 1, 1+sumdiv(n, d, if ((d > 1) && (d % 2), a(n/d)^d))); \\ _Michel Marcus_, Mar 10 2018
%Y A300647 Cf. A003238, A006241, A063834, A069283, A273873, A281145, A289078, A289079, A289501, A298118, A300436, A300439, A300574, A300648, A300649, A300650.
%K A300647 nonn
%O A300647 1,3
%A A300647 _Gus Wiseman_, Mar 10 2018