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A349148
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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.
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2
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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
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OFFSET
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0,3
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LINKS
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EXAMPLE
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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.
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PROG
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(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
(0..n).map{|i| A(i)}
end
(Python)
from math import lcm
from itertools import combinations_with_replacement
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
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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