A305572 a(n) = (-1)^(n-1) + Sum_{d|n, d>1} a(n/d)^d.

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, 32, 2, 3940, 2, 0, 2058, 4, 162, 102944, 2, 4, 8202, 1536, 2, 51940, 2, 32, 207370, 4, 2, 3538944, 130, 3204, 131082, 32, 2, 15668836, 2082, 1536, 524298, 4, 2, 54327840

Offset: 1

Author

Gus Wiseman, Jun 05 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..6911

Crossrefs

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

Programs

Mathematica

a[n_]:=a[n]=(-1)^(n-1)+Sum[a[n/y]^y,{y,Divisors[n]//Rest}];
Array[a,40]

PARI

A305572(n) = ((-1)^(n-1) + sumdiv(n,d,if(d==1,0,A305572(n/d)^d))); \\ Antti Karttunen, Dec 05 2021

Formula

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.