|
|
A349145
|
|
Number of ordered n-tuples (x_1, x_2, x_3, ..., x_n) such that Sum_{k=1..n} k/x_k is an integer and x_k is an integer between 1 and n for 1 <= k <= n.
|
|
2
|
|
|
1, 1, 2, 8, 43, 207, 2391, 15539, 182078, 2070189, 35850460, 338695058, 10609401552, 115445915555
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
EXAMPLE
|
1/1 + 2/1 = 3 and 3 is an integer.
1/1 + 2/2 = 2 and 2 is an integer.
1/2 + 2/1 = 5/2.
1/2 + 2/2 = 3/2.
So a(2) = 2.
|
|
PROG
|
(Ruby)
def A(n)
return 1 if n == 0
cnt = 0
(1..n).to_a.repeated_permutation(n){|i|
cnt += 1 if (1..n).inject(0){|s, j| s + j / i[j - 1].to_r}.denominator == 1
}
cnt
end
(0..n).map{|i| A(i)}
end
(Python)
from fractions import Fraction
from itertools import product
def A349145(n): return sum(1 for d in product(range(1, n+1), repeat=n) if sum(Fraction(i+1, j) for i, j in enumerate(d)).denominator == 1) # Chai Wah Wu, Nov 09 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|