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A144757
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Number of factor trees for n.
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0
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1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 2, 5, 1, 6, 1, 6, 2, 2, 1, 20, 1, 2, 2, 6, 1, 12, 1, 14, 2, 2, 2, 30, 1, 2, 2, 20, 1, 12, 1, 6, 6, 2, 1, 70, 1, 6, 2, 6, 1, 20, 2, 20, 2, 2, 1, 60, 1, 2, 6, 42, 2, 12, 1, 6, 2, 12, 1, 140, 1, 2, 6, 6, 2, 12, 1, 70, 5, 2, 1, 60, 2, 2, 2, 20, 1, 60, 2, 6, 2, 2, 2, 252
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,5
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COMMENTS
| A factor tree for n is a binary tree, with the root labeled with n and the terminal nodes labeled with primes, such that each non-terminal node is the product of its two child nodes. This is the number of prime factorizations of n, ignoring the commutativity and associativity of multiplication.
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EXAMPLE
| a(12)=6 because 12 can be factored as (2*2)*3, (2*3)*2, (3*2)*2, 2*(2*3), 2*(3*2) and 3*(2*2).
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CROSSREFS
| a(n) = A000108(A001222(n)-1) * A008480(n)
Sequence in context: A020738 A063279 A124333 * A002107 A133099 A006571
Adjacent sequences: A144754 A144755 A144756 * A144758 A144759 A144760
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KEYWORD
| easy,nonn
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AUTHOR
| David Radcliffe (dradcliffe(AT)gmail.com), Sep 20 2008
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