Abstract
Let A be a sequence of natural numbers, rA(n) be the number of ways to represent n as a sum of consecutive elements in A, and MA(x) ≔ ∑n ≤ x rA(n). We give a new short proof of LeVeque's formula regarding MA(x) when A is an arithmetic progression, and then extend the proof to give asymptotic formulas for the case when A behaves almost like an arithmetic progression, and also when A is the set of primes in an arithmetic progression.
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