A325612 - OEIS

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A325612

Width (number of leaves) of the rooted tree with Matula-Goebel number 2^n - 1.

1, 1, 2, 2, 1, 4, 1, 4, 5, 3, 6, 7, 4, 5, 7, 6, 7, 11, 7, 7, 9, 10, 7, 13, 7, 11, 9, 11, 11, 13, 11, 12, 15, 16, 10, 19, 19, 15, 18, 16, 16, 18, 10, 18, 18, 17, 15, 21, 15, 18, 24, 23, 19, 23, 25, 25, 18, 26, 25, 28

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

OFFSET

1,3

COMMENTS

Every positive integer has a unique q-factorization (encoded by A324924) into factors q(i) = prime(i)/i, i > 0. For example:

11 = q(1) q(2) q(3) q(5)

50 = q(1)^3 q(2)^2 q(3)^2

360 = q(1)^6 q(2)^3 q(3)

For n > 1, a(n) is the multiplicity of q(1) = 2 in the q-factorization of 2^n - 1.

LINKS

Table of n, a(n) for n=1..60.

Keith Briggs, Matula numbers and rooted trees.