A326441 Number of subsets of {1..n} whose sum is equal to the product of their complement.
0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 3, 1, 2, 1, 3, 3, 3, 3, 1, 4, 4, 3, 2, 2, 4, 3, 5, 3, 2, 4, 5, 4, 5, 6, 1, 4, 2, 5, 4, 7, 4, 4, 3, 3, 6, 14, 3, 4, 10, 6, 3, 6, 4, 4, 4, 8, 7, 6, 8, 7, 10, 5, 11, 8, 5, 11, 4, 7, 7, 5, 8, 12, 5, 6, 9, 8, 11, 8, 5, 8, 9, 8, 10, 8
Offset: 0
Keywords
Examples
The initial terms count the following subsets:
1: {1}
3: {1,2}
5: {3,5}
6: {3,4,5}
7: {2,4,5,7}
8: {2,4,5,6,7}
9: {2,3,5,6,7,9}
10: {4,5,6,8,9,10}
10: {2,3,5,6,7,8,9}
10: {1,2,3,4,5,8,9,10}
Also the number of subsets of {1..n} whose product is equal to the sum of their complement. For example, the initial terms count the following subsets:
1: {}
3: {3}
5: {1,2,4}
6: {1,2,6}
7: {1,3,6}
8: {1,3,8}
9: {1,4,8}
10: {6,7}
10: {1,4,10}
10: {1,2,3,7}
Links
- Giovanni Resta, Table of n, a(n) for n = 0..500
Crossrefs
Programs
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Maple
b:= proc(n, s, p) `if`(s=p, 1, `if`(n<1, 0, b(n-1, s, p)+ `if`(s-n -
Mathematica
Table[Length[Select[Subsets[Range[n]],Plus@@#==Times@@Complement[Range[n],#]&]],{n,0,10}]
Extensions
a(21)-a(83) from Giovanni Resta, Jul 08 2019
Comments