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