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A379672
Number of finite sets of positive integers with sum + product = n.
17
0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 3, 2, 1, 3, 3, 1, 2, 3, 2, 3, 3, 2, 3, 3, 3, 4, 3, 1, 2, 4, 4, 4, 3, 2, 4, 3, 1, 5, 5, 2, 3, 4, 3, 3, 5, 5, 4, 2, 1, 5, 6, 3, 4, 4, 3, 4, 3, 2, 4, 6, 4, 5, 6, 3, 4, 5, 4, 4, 4, 5, 5, 2, 2, 6, 7, 4, 3, 5
OFFSET
0,12
COMMENTS
Antidiagonal sums of A379671, starting with 0.
The only zeros are a(0) and a(3).
EXAMPLE
The a(n) sets for n = 2, 11, 20, 35, 47, 60:
{1} {1,5} {10} {3,8} {5,7} {30}
{2,3} {2,6} {1,17} {1,23} {1,5,9}
{1,3,4} {2,11} {2,15} {2,4,6}
{1,4,6} {3,11} {1,2,19}
{2,3,6} {1,3,14}
{1,4,11}
MATHEMATICA
Table[Length[Select[Join@@Array[IntegerPartitions, n, 0], UnsameQ@@#&&Total[#]+Times@@#==n&]], {n, 0, 30}]
CROSSREFS
Arrays counting multisets by sum and product:
- partitions: A379666, antidiagonal sums A379667
- partitions without ones: A379668, antidiagonal sums A379669 (zeros A379670)
- strict partitions: A379671, antidiagonal sums A379672 (this)
- strict partitions without ones: A379678, antidiagonal sums A379679 (zeros A379680)
Counting and ranking multisets by comparing sum and product:
- same: A001055 (strict A045778), ranks A301987
- divisible: A057567, ranks A326155
- divisor: A057568, ranks A326149, see A326156, A326172, A379733
- greater: A096276 shifted right, ranks A325038
- greater or equal: A096276, ranks A325044
- less: A114324, ranks A325037, see A318029
- less or equal: A319005, ranks A379721
- different: A379736, ranks A379722, see A111133
A000041 counts integer partitions, strict A000009.
A025147 counts strict partitions into parts > 1, non-strict A002865.
A318950 counts factorizations by sum.
Sequence in context: A024693 A025126 A129706 * A160384 A178305 A338621
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 03 2025
EXTENSIONS
More terms from Jinyuan Wang, Jan 11 2025
STATUS
approved