A305572 - OEIS

%I #11 Dec 06 2021 03:08:17

%S 1,0,2,0,2,4,2,0,10,4,2,32,2,4,42,0,2,228,2,32,138,4,2,1536,34,4,1514,

%T 32,2,3940,2,0,2058,4,162,102944,2,4,8202,1536,2,51940,2,32,207370,4,

%U 2,3538944,130,3204,131082,32,2,15668836,2082,1536,524298,4,2,54327840

%N a(n) = (-1)^(n-1) + Sum_{d|n, d>1} a(n/d)^d.

%H Antti Karttunen, <a href="/A305572/b305572.txt">Table of n, a(n) for n = 1..6911</a>

%F a(n) = Sum_t (-1)^(n-k) where the sum is over all same-trees of weight n (see A281145 for definition) and k is the number of leaves.

%t a[n_]:=a[n]=(-1)^(n-1)+Sum[a[n/y]^y,{y,Divisors[n]//Rest}];

%t Array[a,40]

%o (PARI) A305572(n) = ((-1)^(n-1) + sumdiv(n,d,if(d==1,0,A305572(n/d)^d))); \\ _Antti Karttunen_, Dec 05 2021

%Y Cf. A196545, A273873, A281145, A289078, A289079, A289501, A290261, A290971, A291441, A300862-A300866.

%K nonn

%O 1,3

%A _Gus Wiseman_, Jun 05 2018