A281145 Number of same-trees of weight n.

1, 2, 2, 6, 2, 14, 2, 54, 10, 38, 2, 494, 2, 134, 42, 4470, 2, 3422, 2, 10262, 138, 2054, 2, 490926, 34, 8198, 1514, 314294, 2, 628318, 2, 30229110, 2058, 131078, 162, 150147342, 2, 524294, 8202, 628073814, 2, 109952254, 2, 371210294, 207370, 8388614, 2

Offset: 1

Author

Gus Wiseman, Jan 15 2017

Keywords

• nonn

Comments

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.

Examples

			The a(6)=14 same-trees are:
6,
(33),
(222),
(3(111)), ((111)3),
(22(11)), (2(11)2), ((11)22),
(2(11)(11)), ((11)2(11)), ((11)(11)2),
((111)(111)), ((11)(11)(11)), (111111).
The a(9)=10 same-trees are:
9,
(333),
(33(111)), (3(111)3), ((111)33),
(3(111)(111)), ((111)3(111)), ((111)(111)3),
((111)(111)(111)), (111111111).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A196545, A260685, A273873, A275870, A006241.

Programs

Mathematica

a[n_]:=1+DivisorSum[n,b[#]^(n/#)&]-b[n]/.b->a;
Array[a,47]

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

Formula

a(n) = 1 + Sum a(d)^(n/d) where the sum is over divisors less than n.