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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 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 December 10 23:18 EST 2019. Contains 329910 sequences. (Running on oeis4.)