A349148 Number of unordered n-tuples {x_1, x_2, x_3, ..., x_n} such that Sum_{k=1..n} 1/x_k is an integer and x_k is an integer between 1 and n for 1 <= k <= n.

1, 1, 2, 3, 6, 9, 25, 39, 84, 158, 381, 610, 2175, 3489, 7252, 24744, 54658, 89031, 273604, 443746, 1690517, 5261990, 9399018, 15470605, 58261863, 102574465

Offset: 0

Author

Seiichi Manyama, Nov 08 2021

Keywords

• nonn
• more

Examples

			1/1 + 1/1 = 2 and 2 is an integer.
1/1 + 1/2 = 3/2.
1/2 + 1/2 = 1 and 1 is an integer.
So a(2) = 2.
		

Crossrefs

Cf. A349146.

Programs

Python

from math import lcm
from itertools import combinations_with_replacement
def A349148(n):
    k = lcm(*range(2,n+1))
    dlist = (k//d for d in range(1,n+1))
    return sum(1 for d in combinations_with_replacement(dlist,n) if sum(d) % k == 0) # Chai Wah Wu, Nov 09 2021

Ruby

def A(n)
  return 1 if n == 0
  cnt = 0
  (1..n).to_a.repeated_combination(n){|i|
    cnt += 1 if (1..n).inject(0){|s, j| s + 1 / i[j - 1].to_r}.denominator == 1
  }
  cnt
end
def A349148(n)
  (0..n).map{|i| A(i)}
end
p A349148(10)

Extensions

a(16)-a(25) from Alois P. Heinz, Nov 08 2021