A300647 - OEIS

%I #11 May 31 2021 17:46:29

%S 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 42,2,1,2058,2,162,10,2,2,8202,2,2,138,2,2,207370,2,2,2,130,34,131082,

%U 2,2,1514,2082,2,524298,2,2,42,2,2,14725738,1,8226,2058,2

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

%C 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 Antti Karttunen, <a href="/A300647/b300647.txt">Table of n, a(n) for n = 1..8192</a>

%F a(n) = 1 + Sum_d a(n/d)^d where the sum is over odd divisors of n greater than 1.

%e The a(9) = 10 odd same-trees:

%e 9,

%e (333),

%e (33(111)), (3(111)3), ((111)33)

%e (3(111)(111)), ((111)3(111)), ((111)(111)3),

%e ((111)(111)(111)), (111111111).

%t a[n_]:=1+Sum[a[n/d]^d,{d,Select[Rest[Divisors[n]],OddQ]}];

%t Array[a,80]

%o (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 Cf. A003238, A006241, A063834, A069283, A273873, A281145, A289078, A289079, A289501, A298118, A300436, A300439, A300574, A300648, A300649, A300650.

%K nonn

%O 1,3

%A _Gus Wiseman_, Mar 10 2018