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 A303878 Consider the representation of some integer (>1) as the sum of distinct unit fraction (<1). The sum of these denominators is least. 0
 2, 3, 4, 5, 6, 8, 9, 10, 15, 18, 20, 24 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Consider the representation of 1 as the sum of distinct unit fraction (<1). We can easily found the least sum of the denominators. The solution is 1 = 1/2 + 1/3 + 1/6. LINKS Table of n, a(n) for n=1..12. EXAMPLE Denominators | Sum ---------------------------------------------+----- 2, 3, 4, 5, 6, 8, 9, 10, 15, 18, 20, 24 | 124 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 28 | 126 2, 3, 4, 5, 6, 7, 9, 12, 14, 18, 20, 28 | 128 2, 3, 4, 5, 6, 8, 9, 10, 12, 18, 24, 30 | 131 2, 3, 4, 5, 6, 7, 8, 12, 14, 20, 24, 28 | 133 PROG (Ruby) def partition(n, min, max) return [[]] if n == 0 [max, n].min.downto(min).flat_map{|i| partition(n - i, min, i - 1).map{|rest| [i, *rest]}} end def f(n) a = [] partition(n, 2, n).each{|ary| sum = ary.inject(0){|s, i| s + 1 / i.to_r} a << ary.reverse if sum.denominator == 1 && sum.numerator > 1 } a end n = 1 a = [] while a == [] n += 1 a = f(n) end p a CROSSREFS Sequence in context: A256007 A324689 A280578 * A039170 A097624 A000398 Adjacent sequences: A303875 A303876 A303877 * A303879 A303880 A303881 KEYWORD nonn,fini,full AUTHOR Seiichi Manyama, May 02 2018 STATUS approved

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Last modified November 28 22:38 EST 2023. Contains 367422 sequences. (Running on oeis4.)