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A069016
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Look at all the different ways to factorize n as a product of numbers bigger than 1, and for each factorization write down the sum of the factors; a(n) = number of different sums.
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0
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1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 3, 1, 4, 1, 3, 2, 2, 1, 5, 2, 2, 3, 3, 1, 5, 1, 4, 2, 2, 2, 7, 1, 2, 2, 5, 1, 5, 1, 3, 4, 2, 1, 8, 2, 4, 2, 3, 1, 7, 2, 5, 2, 2, 1, 9, 1, 2, 4, 6, 2, 5, 1, 3, 2, 5, 1, 10, 1, 2, 4, 3, 2, 5, 1, 8, 5, 2, 1, 8, 2, 2, 2, 5, 1, 10, 2, 3, 2, 2, 2, 12, 1, 4, 4, 7, 1, 5, 1
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OFFSET
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1,6
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REFERENCES
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Amarnath Murthy, Generalization of Partition Function and Introducing Smarandache Factor Partitions, Smarandache Notions Journal, Vol. 11, 1-2-3. Spring 2000.
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LINKS
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Table of n, a(n) for n=1..103.
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EXAMPLE
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The factorizations of 30 are (2,3,5), (2,15), (3,10), (5,6) and (30), which have the 5 distinct sums 10, 17, 13, 11 and 30. Hence a(30) = 5.
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CROSSREFS
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Cf. A034891.
Sequence in context: A209402 A082641 A138553 * A211270 A071414 A067148
Adjacent sequences: A069013 A069014 A069015 * A069017 A069018 A069019
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 01 2002
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EXTENSIONS
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Edited by David W. Wilson, May 27, 2002.
Edited by N. J. A. Sloane, Apr 28 2013
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STATUS
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approved
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