OFFSET
1,2
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.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..4000
FORMULA
a(n) = 1 + Sum a(d)^(n/d) where the sum is over divisors less than n.
EXAMPLE
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).
MATHEMATICA
a[n_]:=1+DivisorSum[n, b[#]^(n/#)&]-b[n]/.b->a;
Array[a, 47]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 15 2017
STATUS
approved