把正整数n倒过来写得到N，N/n不是无限小数

manthanein

不考虑\(n\)的末位为0的情况。以下几种是显然的：
（1）n是回文数。
（2）n是1089、2178及其衍生。
（3）n是2的幂或者5的幂。
其他的呢？
我用excel试了下，81/18，21/12，51/15，42/24……等等。越大似乎越少了，做到的最大的是57831/13875。
有什么规律吗？

mathe

2的幂，5的幂再乘以3，9或11显然也都可以。

zeroieme

暴力

1. ParallelCombine[Select[#,({#,#//IntegerDigits}//Which[#[[-1,-1]]==0,False,(#[[2]]//Reverse)==#[[2]],False,(#[[2]]//Reverse//FromDigits)/#[[1]]//Denominator//FactorInteger//#[[All,1]]&//Complement[#,{1,2,5}]&//#!={}&,False,True,True]&)&]&,Range[10^8]]

复制代码

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