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Let Δ(x) be the error term associated with the asymptotic formula for the counting function on the set of numbers that are sums of three squares. We give a formula for Δ(x) and use it to prove that Δ(x) has average order and normal order 3 1og x/(16 1og 2).
Let C′(x) denote the number of integers n ⩽ x such that there is no non‐abelian group of order n, but there exists a non‐cyclic group of order n. Here it is shown that
C′(x)∼e−γxlog log x(log log log x)2,x→∞,
where γ denotes Euler's constant.
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