渐近估计式(sum form n≤x) φ(n)=(3/π~2)x^2+O(xlogx)的推广

The extension on the asymptotic estimation formula (sum form n≤x) φ(n)=(3/π~2)x^2+O(xlogx)

设φ(n)是 Euler函数 ,本文将渐近估计式 ∑n≤ xφ(n) =3π2 x2 +O(xlogx) (x >2 )进行了一系列推广 ,给出了∑n≤ xnαφ(n) ,∑n≤ x(-1 ) n- 1 nαφ(n) ,∑n≤ xp | nnαφ(n) ,∑n≤ xp | nnαφ(n)

Let \$φ((n)\$ be Euler's function, in this paper, the asymptotic estimation formula \$∑n≤xφ(n)=3\%π\+2\%x\+2+O(x\%log\%x)(x>2)\$ is extended successively. The asymptotic estimation formulas are give on summations \$∑n≤xn\+αφ(n),∑n≤x(-1)\+\{n-1\}n\+αφ(n),∑n≤xp|nn\+αφ(n)\$ and \$∑n≤xpnn\+αφ(n)\$ etc.