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%I #32 Jul 15 2023 14:02:05
%S 1,1,2,8,43,207,2391,15539,182078,2070189,35850460,338695058,
%T 10609401552,115445915555
%N 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.
%e 1/1 + 2/1 = 3 and 3 is an integer.
%e 1/1 + 2/2 = 2 and 2 is an integer.
%e 1/2 + 2/1 = 5/2.
%e 1/2 + 2/2 = 3/2.
%e So a(2) = 2.
%o (Ruby)
%o def A(n)
%o return 1 if n == 0
%o cnt = 0
%o (1..n).to_a.repeated_permutation(n){|i|
%o cnt += 1 if (1..n).inject(0){|s, j| s + j / i[j - 1].to_r}.denominator == 1
%o }
%o cnt
%o end
%o def A349145(n)
%o (0..n).map{|i| A(i)}
%o end
%o p A349145(6)
%o (Python)
%o from fractions import Fraction
%o from itertools import product
%o 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
%Y Cf. A073090, A349146.
%K nonn,more
%O 0,3
%A _Seiichi Manyama_, Nov 08 2021
%E a(10)-a(13) from _Alois P. Heinz_, Nov 08 2021
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