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

1,6

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

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

Cf. A001055, A034891.

Sequence in context: A342462 A239140 A138553 * A211270 A071414 A067148

Adjacent sequences: A069013 A069014 A069015 * A069017 A069018 A069019

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