سەرچاوەی ژمارەی ھاوڕێ ببینە

لە [[تیۆریی ژمارەکان]]دا '''ژمارەی ھاوڕێ''' ({{بە ئینگلیزی|Friendly number}}) بە دوو ژمارە دەوترێت کە ڕێژەی سەرجەمی [[بەشدراو|بەشدراوەکانیان]] بە ژمارەکە خۆی لەگەڵ یەک یان چەن ژمارەی تر یەکسانە. بەو دوو ژمارەیەی ئەم تایبەتمەندییەیان ھەیە، دەوترێت جووتە ھاوڕێ. ژمارەیەک کە ھاوڕێی لەم شێوەیەی نەبێت، پێی دەوترێت '''ژمارەی تەنیا'''.  
ڕێژەی سەرجەمی بەشدراوەکان بە ژمارەکە خۆی، بە زمانی بیرکاری بەم شێوە <math> \tfrac{\sigma(n)}{n}</math> دەردەبڕن لێرەدا <math>{\sigma}</math> سەرجەمی بەشدراوەکان دەنوێنێت. 

ژمارەکانی ١ تا ٥ ھەموویان تەنیان. بچووکترین ژمارەی ھاوڕێ، بریتییە لە ژمارە  ٦ و جووتە ھاوڕێکەی بەم شێوە دەردەبڕن <math>(6,28)</math> لێرەدا <math> \tfrac{\sigma(6)}{6}</math> یەکسانە بە <math>\tfrac{1+2+3+6}{6}=2</math> بە ھەمان شێوە <math> \tfrac{\sigma(28)}{28}</math> یەکسانە بە <math>\tfrac{1+2+4+7+14+28}{28}=2</math> وەک دەبینرێت، بەھای<math> \tfrac{\sigma(6)}{6}</math> و بەھای <math> \tfrac{\sigma(28)}{28}</math> یەکسانە بە ٢ واتە ٦ و ٢٨ ھاوڕێن.
== نموونە ==
بۆ نموونە ٣٠ و ١٤٠ دوو ژمارەی ھاوڕێن لەبەر ئەوەی، 
{{Ltr}}
:<math> \tfrac{\sigma(30)}{30} = \tfrac{1+2+3+5+6+10+15+30}{30} = \tfrac{12}{5}</math>
:<math> \tfrac{\sigma(140)}{140} = \tfrac{1+2+4+5+7+10+14+20+28+35+70+140}{140} = \tfrac{12}{5}.</math>
{{Ltr/end}}

لە خشتەی خوارەوەدا، ژمارە شینەکان، ھاوڕێن. ژمارە سوورەکان، Coprime، و ئەو ژمارانەی بە بەکگراوندێکی زەرد تیشکیان لەسەر دراوە، باری نادیاریان ھەیە.
{| class="wikitable sortable mw-collapsible mw-collapsed"
|+
|-
|''n''
|<math>\sigma(n)</math>
|<math>\frac{\sigma(n)}{n}</math>
|rowspan="37" style="border: none; background: none;" |
|''n''
|<math>\sigma(n)</math>
|<math>\frac{\sigma(n)}{n}</math>
|rowspan="37" style="border: none; background: none;" |
|''n''
|<math>\sigma(n)</math>
|<math>\frac{\sigma(n)}{n}</math>
|rowspan="37" style="border: none; background: none;" |
|''n''
|<math>\sigma(n)</math>
|<math>\frac{\sigma(n)}{n}</math>
|-
|1
|1
|1
|37
|38
|38/37
|73
|74
|74/73
|109
|110
|110/109
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|2
|3
|3/2
|{{background color|yellow|38}}
|{{background color|yellow|60}}
|{{background color|yellow|30/19}}
|{{background color|yellow|74}}
|{{background color|yellow|114}}
|{{background color|yellow|57/37}}
|{{background color|yellow|110}}
|{{background color|yellow|216}}
|{{background color|yellow|108/55}}
|-
|3
|4
|4/3
|39
|56
|56/39
|75
|124
|124/75
|111
|152
|152/111
|-
|4
|7
|7/4
|{{color|blue|40}}
|{{color|blue|90}}
|{{color|blue|9/4}}
|{{background color|yellow|76}}
|{{background color|yellow|140}}
|{{background color|yellow|35/19}}
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|{{background color|yellow|248}}
|{{background color|yellow|31/14}}
|-
|5
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|6/5
|41
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|42/41
|77
|96
|96/77
|113
|114
|114/113
|-
|{{color|blue|6}}
|{{color|blue|12}}
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|{{color|blue|42}}
|{{color|blue|96}}
|{{color|blue|16/7}}
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|{{color|blue|168}}
|{{color|blue|28/13}}
|{{color|blue|114}}
|{{color|blue|240}}
|{{color|blue|40/19}}
|-
|7
|8
|8/7
|43
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|79
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|80/79
|115
|144
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|-
|8
|15
|15/8
|{{background color|yellow|44}}
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|{{color|blue|80}}
|{{color|blue|186}}
|{{color|blue|93/40}}
|{{background color|yellow|116}}
|{{background color|yellow|210}}
|{{background color|yellow|105/58}}
|-
|9
|13
|13/9
|{{color|red|45}}
|{{color|red|78}}
|{{color|red|26/15}}
|81
|121
|121/81
|{{background color|yellow|117}}
|{{background color|yellow|182}}
|{{background color|yellow|14/9}}
|-
|{{background color|yellow|10}}
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|{{background color|yellow|72}}
|{{background color|yellow|36/23}}
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|{{background color|yellow|126}}
|{{background color|yellow|63/41}}
|{{background color|yellow|118}}
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|{{background color|yellow|90/59}}
|-
|11
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|12/11
|47
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|83
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|84/83
|119
|144
|144/119
|-
|{{color|blue|12}}
|{{color|blue|28}}
|{{color|blue|7/3}}
|{{color|red|48}}
|{{color|red|124}}
|{{color|red|31/12}}
|{{color|blue|84}}
|{{color|blue|224}}
|{{color|blue|8/3}}
|{{color|blue|120}}
|{{color|blue|360}}
|{{color|blue|3}}
|-
|13
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|14/13
|49
|57
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|85
|108
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|133
|133/121
|-
|{{background color|yellow|14}}
|{{background color|yellow|24}}
|{{background color|yellow|12/7}}
|50
|93
|93/50
|{{background color|yellow|86}}
|{{background color|yellow|132}}
|{{background color|yellow|66/43}}
|{{background color|yellow|122}}
|{{background color|yellow|186}}
|{{background color|yellow|93/61}}
|-
|{{background color|yellow|15}}
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|-
|16
|31
|31/16
|{{color|red|52}}
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|{{color|red|49/26}}
|{{background color|yellow|88}}
|{{background color|yellow|180}}
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|-
|17
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|53
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|89
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|125
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|-
|{{color|red|18}}
|{{color|red|39}}
|{{color|red|13/6}}
|{{background color|yellow|54}}
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|{{background color|yellow|90}}
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|{{background color|yellow|13/5}}
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|19
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|55
|72
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|{{background color|yellow|91}}
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|127
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|{{background color|yellow|20}}
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|{{background color|yellow|21/10}}
|{{color|blue|56}}
|{{color|blue|120}}
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|{{background color|yellow|92}}
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|128
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|21
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|23
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|-
|{{color|blue|24}}
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|{{color|blue|14/5}}
|{{color|blue|96}}
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|{{color|blue|21/8}}
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|{{color|blue|28/11}}
|-
|25
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|61
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|97
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|{{background color|yellow|26}}
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|{{background color|yellow|96}}
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|98
|171
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|{{background color|yellow|134}}
|{{background color|yellow|204}}
|{{background color|yellow|102/67}}
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|27
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|63
|104
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|{{background color|yellow|99}}
|{{background color|yellow|156}}
|{{background color|yellow|52/33}}
|{{color|blue|135}}
|{{color|blue|240}}
|{{color|blue|16/9}}
|-
|{{color|blue|28}}
|{{color|blue|56}}
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|64
|127
|127/64
|100
|217
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|{{color|red|136}}
|{{color|red|270}}
|{{color|red|135/68}}
|-
|29
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|65
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|101
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|{{color|blue|30}}
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|{{background color|yellow|108/71}}
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|35
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|144
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|}
== فانکشنی دابەشکردن ==
ئەگەر <math>n</math> ژمارەیەکی  ئەرێنی [[ژمارەی سروشتی|سروشتی]] بێت <math>{\sigma(n)}</math>  دەکاتە سەرجەمی [[بەشدراو|بەشدراوەکانی]] ژمارەکە. بۆ نموونە  بەشدراوەکانی ١٠ بریتین لە١، ٢، ٥، ١٠ لەمەوە سەرجەمی بەشدراوەکانی ١٠ دەکاتە <math>{\sigma(10)}=1+2+5+10=18</math>
== سەرچاوەکان ==
{{سەرچاوەکان}}
* {{بیرخستنەوەی ویکی | بەستەر= https://en.wikipedia.org/wiki/Friendly_number| سەردێڕ=Friendly number | زمان= ئینگلیزی | سەردان= ١٦ی ئازاری ٢٠٢١}}

== بەستەرە دەرەکییەکان ==

{{تووڵی دەروازە|ماتماتیک|تیۆریی ژمارەکان}}

{{ژمارە-کۆلکە}}

[[پۆل:پاشیەکیی ژمارە تەواوەکان]]