A349146 -id:A349146 - cp's OEIS frontend

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.

1, 1, 2, 8, 43, 207, 2391, 15539, 182078, 2070189, 35850460, 338695058, 10609401552, 115445915555

Offset: 0

Seiichi Manyama, Nov 08 2021

			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.

Cf. A073090, A349146.

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

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
def A349145(n)
  (0..n).map{|i| A(i)}
end
p A349145(6)

a(10)-a(13) from Alois P. Heinz, Nov 08 2021

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.

Original entry on oeis.org

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

Seiichi Manyama, Nov 08 2021

			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.

Cf. A349146.

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

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)

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

cp's OEIS Frontend

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.

Views

Author

Keywords

Examples

Crossrefs

Programs

Python

Ruby

Extensions