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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.

%I A349148 #39 Jul 15 2023 14:02:13
%S A349148 1,1,2,3,6,9,25,39,84,158,381,610,2175,3489,7252,24744,54658,89031,
%T A349148 273604,443746,1690517,5261990,9399018,15470605,58261863,102574465
%N 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.
%e A349148 1/1 + 1/1 = 2 and 2 is an integer.
%e A349148 1/1 + 1/2 = 3/2.
%e A349148 1/2 + 1/2 = 1 and 1 is an integer.
%e A349148 So a(2) = 2.
%o A349148 (Ruby)
%o A349148 def A(n)
%o A349148   return 1 if n == 0
%o A349148   cnt = 0
%o A349148   (1..n).to_a.repeated_combination(n){|i|
%o A349148     cnt += 1 if (1..n).inject(0){|s, j| s + 1 / i[j - 1].to_r}.denominator == 1
%o A349148   }
%o A349148   cnt
%o A349148 end
%o A349148 def A349148(n)
%o A349148   (0..n).map{|i| A(i)}
%o A349148 end
%o A349148 p A349148(10)
%o A349148 (Python)
%o A349148 from math import lcm
%o A349148 from itertools import combinations_with_replacement
%o A349148 def A349148(n):
%o A349148     k = lcm(*range(2,n+1))
%o A349148     dlist = (k//d for d in range(1,n+1))
%o A349148     return sum(1 for d in combinations_with_replacement(dlist,n) if sum(d) % k == 0) # _Chai Wah Wu_, Nov 09 2021
%Y A349148 Cf. A349146.
%K A349148 nonn,more
%O A349148 0,3
%A A349148 _Seiichi Manyama_, Nov 08 2021
%E A349148 a(16)-a(25) from _Alois P. Heinz_, Nov 08 2021