A325544 - OEIS

A325544

Number of nodes in the rooted tree with Matula-Goebel number n!.

1, 1, 2, 4, 6, 9, 12, 15, 18, 22, 26, 30, 34, 38, 42, 47, 51, 55, 60, 64, 69, 74, 79, 84, 89, 95, 100, 106, 111, 116, 122, 127, 132, 138, 143, 149, 155, 160, 165, 171, 177, 182, 188, 193, 199, 206, 212, 218, 224, 230, 237, 243, 249, 254, 261, 268, 274, 280

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OFFSET

0,3

COMMENTS

Also one plus the number of factors in the factorization of n! into factors q(i) = prime(i)/i. For example, the q-factorization of 7! is 7! = q(1)^9 * q(2)^3 * q(3) * q(4), with 14 = a(7) - 1 factors.

LINKS

Table of n, a(n) for n=0..57.

FORMULA

For n > 1, a(n) = 1 - n + Sum_{k = 1..n} A061775(k).

EXAMPLE

Matula-Goebel trees of the first 9 factorial number are:

0!: o

1!: o

2!: (o)

3!: (o(o))

4!: (ooo(o))

5!: (ooo(o)((o)))