A317994 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A317994

Number of inequivalent leaf-colorings of the free pure symmetric multifunction with e-number n.

1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 4, 2, 2, 2, 1, 4, 2, 2, 2, 2, 1, 2, 4, 2, 2, 2, 2, 2, 1, 2, 5, 4, 2, 2, 2, 2, 2, 1, 2, 5, 4, 2, 2, 2, 2, 2, 2, 1, 2, 5, 4, 2, 2, 2, 2, 2, 2, 1, 5, 2, 5, 4, 2, 2, 2, 2, 2, 2, 1, 5, 2, 5, 4, 2, 2, 4, 2, 2, 2, 2, 1, 5

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

OFFSET

1,4

COMMENTS

If n = 1 let e(n) be the leaf symbol "o". Given a positive integer n > 1 we construct a unique free pure symmetric multifunction (with empty expressions allowed) e(n) with one atom by expressing n as a power of a number that is not a perfect power to a product of prime numbers: n = rad(x)^(prime(y_1) * ... * prime(y_k)) where rad = A007916. Then e(n) = e(x)[e(y_1), ..., e(y_k)]. For example, e(21025) = o[o[o]][o] because 21025 = rad(rad(1)^prime(rad(1)^prime(1)))^prime(1).

LINKS

Table of n, a(n) for n=1..87.

EXAMPLE

Inequivalent representatives of the a(441) = 11 colorings of the expression e(441) = o[o,o][o] are the following.

1[1,1][1]

1[1,1][2]

1[1,2][1]

1[1,2][2]

1[1,2][3]

1[2,2][1]

1[2,2][2]

1[2,2][3]