On Δ(𝑥,𝑛)=𝜙(𝑥,𝑛) -𝑥𝜙(𝑛)/𝑛

Suryanarayana, D.

doi:10.1090/S0002-9939-1974-0332636-5

On $\Delta (x, n)=\phi (x, n)$ $-x\phi (n)/n$
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by D. Suryanarayana

Proc. Amer. Math. Soc. 44 (1974), 17-21

DOI: https://doi.org/10.1090/S0002-9939-1974-0332636-5

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Abstract:

Let $\Delta (x,n) = \varphi (x,n) - x\varphi (n)/n$, where $\varphi (x,n)$ denotes the number of positive integers $\leqq x$ and prime to $n,\varphi (n) = \varphi (n,n)$. In this paper, lower and upper bounds for $\Delta (x,n)$, which hold for all values of $x \geqq 1$ and $n \geqq 2$, are established.

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