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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 (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]

  1[2,3][1]

  1[2,3][2]

  1[2,3][4]

CROSSREFS

Cf. A007916, A052409, A052410, A277576, A277996, A300626, A316112, A317056, A317658, A317765.

Sequence in context: A286574 A329320 A316112 * A128428 A056171 A238949

Adjacent sequences:  A317991 A317992 A317993 * A317995 A317996 A317997

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 18 2018

STATUS

approved

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Last modified November 21 14:18 EST 2019. Contains 329371 sequences. (Running on oeis4.)