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A069016
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.
10
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
OFFSET
1,6
REFERENCES
Amarnath Murthy, Generalization of Partition Function and Introducing Smarandache Factor Partitions, Smarandache Notions Journal, Vol. 11, 1-2-3. Spring 2000.
FORMULA
a(n) <= A001055(n). - David A. Corneth, Oct 21 2017
EXAMPLE
The factorizations of 12 are (2,2,3), (2,6), (3,4), and (12), which have three distinct sums 7, 8, and 12. Hence a(12) = 3. - Antti Karttunen, Oct 21 2017
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.
CROSSREFS
Sequence in context: A342462 A239140 A138553 * A211270 A071414 A067148
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Apr 01 2002
EXTENSIONS
Edited by David W. Wilson, May 27 2002
Edited by N. J. A. Sloane, Apr 28 2013
STATUS
approved