A292127 - OEIS

A292127

a(1) = 1, a(r(n)^k) = 1 + k * a(n) where r(n) is the n-th number that is not a perfect power A007916(n).

1, 2, 3, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 7, 7, 8, 6, 7, 8, 8, 7, 9, 7, 7, 8, 9, 9, 6, 8, 10, 8, 7, 8, 9, 10, 10, 7, 9, 11, 9, 8, 9, 10, 11, 9, 11, 8, 10, 12, 10, 9, 10, 11, 12, 10, 12, 9, 11, 13, 7, 11, 10, 11, 12, 13, 11, 13, 10, 12, 14, 8, 12, 11

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Any positive integer greater than 1 can be written uniquely as a perfect power r(n)^k. We define a planted achiral (or generalized Bethe) tree b(n) for any positive integer greater than 1 by writing n as a perfect power r(d)^k and forming a tree with k branches all equal to b(d). Then a(n) is the number of nodes in b(n).

LINKS

Table of n, a(n) for n=1..77.

EXAMPLE

The first nineteen planted achiral trees are:

(o),

((o)), (oo),

(((o))), ((oo)),

((((o)))), (ooo), ((o)(o)), (((oo))),

(((((o))))), ((ooo)), (((o)(o))), ((((oo)))),

((((((o)))))), (oooo), (((ooo))), ((((o)(o)))), (((((oo))))).

MATHEMATICA

nn=100;