亲密数_在线百科全书查询
亲密数
定义
如果a的因子和等于b，b的因子和等于a，因子包括1但不包括本身，且a不等于b，则称a，b为亲密数对。一般通过叠代编程求出相应的亲密数对。
例子
如编程找出10000以内的亲密数来：
Option Explicit
Dim I As Long, J As Long, X As Long
Private Sub Form_Load()
Me.Show
For I = 1 To 10000
DoEvents
X = Yzh(I)
If X <= 10000 And I < X Then
If Yzh(X) = I Then
Text1 = Text1 & "(" & I & "," & X & ")" & Chr(13) & Chr(10)
YzhOut (I)
YzhOut (X)
End If
End If
Next
Text1 = Text1 & "计算完成"
End Sub
Private Function Yzh(N As Long) As Long
Yzh = 0
For J = 1 To N / 2
If N Mod J = 0 Then Yzh = Yzh + J
Next
End Function
Private Function YzhOut(N As Long) As Long
Dim Yzh As Long
Text1 = Text1 & N & "=1"
Yzh = 1
For J = 2 To N / 2
If N Mod J = 0 Then
Text1 = Text1 & "+" & J
Yzh = Yzh + J
End If
Next
Text1 = Text1 & "=" & Yzh & Chr(13) & Chr(10)
End Function
程序计算结果，有5组亲密数对，程序输出是：
(220,284)
220=1+2+4+5+10+11+20+22+44+55+110=284
284=1+2+4+71+142=220
(1184,1210)
1184=1+2+4+8+16+32+37+74+148+296+592=1210
1210=1+2+5+10+11+22+55+110+121+242+605=1184
(2620,2924)
2620=1+2+4+5+10+20+131+262+524+655+1310=2924
2924=1+2+4+17+34+43+68+86+172+731+1462=2620
(5020,5564)
5020=1+2+4+5+10+20+251+502+1004+1255+2510=5564
5564=1+2+4+13+26+52+107+214+428+1391+2782=5020
(6232,6368)
6232=1+2+4+8+19+38+41+76+82+152+164+328+779+1558+3116=6368
6368=1+2+4+8+16+32+199+398+796+1592+3184=6232
计算完成。
C语言的实现代码：
#include<stdio.h>
#define Max 10000
int fun(int x)
{
int sum=1,i;
for(i=2;i<=x/2;i++)if(x%i==0)sum=sum+i;
return sum;
}
void print(int x,int y)
{
int i;
printf("%d=1",x);
for(i=2;i<=x/2;i++)if(x%i==0)printf("+%d",i);
printf("=%d\",y);
}
int main()
{
int num=1,i,j,sum;
do{
sum=fun(num);
if(sum>num&&sum<=Max&&num==fun(sum))
{
printf("(%d,%d)\",num,sum);
print(num,sum);
print(sum,num);
}
}while(++num<=Max);
return 0;
}
