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.

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

Author

Amarnath Murthy, Apr 01 2002

Keywords

• nonn

Examples

			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.
		

References

• Amarnath Murthy, Generalization of Partition Function and Introducing Smarandache Factor Partitions, Smarandache Notions Journal, Vol. 11, 1-2-3. Spring 2000.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Scheme-program for computing this sequence

Crossrefs

Cf. A001055, A034891.

Formula

a(n) <= A001055(n). - David A. Corneth, Oct 21 2017

Extensions

Edited by David W. Wilson, May 27 2002

Edited by N. J. A. Sloane, Apr 28 2013