Editing Square-free integer (section)

===Table of ''Q''(''x''), {{Sfrac|6|π<sup>2</sup>}}''x'', and ''R''(''x'')   ===

The table shows how  <math> Q(x)</math> and <math>\frac{6}{\pi^2}x</math>  (with the latter rounded to one decimal place) compare at powers of 10.

<math> R(x) = Q(x) -\frac{6}{\pi^2}x </math> , also denoted as <math> \Delta(x) </math>.

:{| class="wikitable" style="text-align: right"
! <math> x </math>
! <math> Q(x) </math>
! <math>  \frac{6}{\pi^2}x</math>
!<math> R(x)</math>
|-
| 10
| 7
| 6.1
| 0.9
|-
| 10<sup>2</sup>
| 61
| 60.8
| 0.2
|-
| 10<sup>3</sup>
| 608
| 607.9
| 0.1
|-
| 10<sup>4</sup>
| 6,083
| 6,079.3
| 3.7
|-
| 10<sup>5</sup>
| 60,794
| 60,792.7
| 1.3
|-
| 10<sup>6</sup>
| 607,926
| 607,927.1
| {{font color|red|−1.3}}
|-
| 10<sup>7</sup>
| 6,079,291
| 6,079,271.0
| 20.0
|-
| 10<sup>8</sup>
| 60,792,694
| 60,792,710.2
| {{font color|red|−16.2}}
|-
| 10<sup>9</sup>
| 607,927,124
| 607,927,101.9
| 22.1
|-
| 10<sup>10</sup>
| 6,079,270,942
|  6,079,271,018.5
| {{font color|red|−76.5}}
|-
| 10<sup>11</sup>
| 60,792,710,280
| 60,792,710,185.4
| 94.6
|-
| 10<sup>12</sup>
| 607,927,102,274
|  607,927,101,854.0
| 420.0
|-
| 10<sup>13</sup>
| 6,079,271,018,294
| 6,079,271,018,540.3
| {{font color|red|−246.3}}
|-
| 10<sup>14</sup>
| 60,792,710,185,947
| 60,792,710,185,402.7
| 544.3
|-
| 10<sup>15</sup>
| 607,927,101,854,103
| 607,927,101,854,027.0
| 76.0
|-
|}
<math> R(x) </math> changes its sign infinitely often as <math> x </math> tends to infinity.<ref>{{cite journal |last1=Minoru |first1=Tanaka |title=Experiments concerning the distribution of squarefree numbers |journal=Proceedings of the Japan Academy, Series A, Mathematical Sciences |year=1979 |volume=55 |issue=3 |doi=10.3792/pjaa.55.101 |s2cid=121862978 |url=https://projecteuclid.org/euclid.pja/1195517398|doi-access=free }}</ref>

The absolute value of <math> R(x) </math> is astonishingly small compared with <math> x </math>.