Which numbers are not the sum plus the product of three positive integers?

2021/12/31 by Conrey, Brian, Shah, Neil
#11D45 #11D72 #11D75 #11N36 #11N56 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2112.15551

Abstract

We investigate the number R₃(n) of representations of n as the sum plus the product of three positive integers. On average, R₃(n) is (1)/(2)log² n. We give an upper bound for R₃(n) and an upper bound for the number of n ≤ N such that R₃(n) = 0. We conjecture that R₃(n)= 0 infinitely often.

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