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A317994
Number of inequivalent leaf-colorings of the free pure symmetric multifunction with e-number n.
9
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
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).
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]
1[2,3][1]
1[2,3][2]
1[2,3][4]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 18 2018
STATUS
approved