Papers › Partitions with prescribed sum of reciprocals: computational results
Partitions with prescribed sum of reciprocals: computational results
Wouter van Doorn
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For a positive rational α, call a set of distinct positive integers {a₁, a₂, …, aᵣ} an α-partition of n, if the sum of the aᵢ is equal to n and the sum of the reciprocals of the aᵢ is equal to α. Define n_α to be the smallest positive integer such that for all n ≥n_α an α-partition of n exists and, for a positive integer M ≥2, define N_M to be the smallest positive integer such that for all n ≥N_M a 1-partition of n exists where M does not divide any of the aᵢ. In this paper we determine N_M for all M ≥2, and find the set of all α such that n_α ≤100.
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