For any positive integer n, let σ (n) and p(n) denote the sum of divisors and the least prime divisor of n respectively. Let a, b be positive integers. In this paper we prove the following two results: (i) If 4|a and gcd(a, b) = 1, then a and b do not satisfy σ (a) = σ (b) = a + b. (ii) If a > 10 8 and p(a) > 2 log 2 a + 1, where log 2 a is the logarithm of a with base 2, then a and b do not satisfy σ (a) = σ (b) = a + b + λ, where λ ∈ {0, ±1}.
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