20亿以内哪个数的约数个数最多，个数是多少？

大家好，又见面了，我是全栈君。

混蛋的百度吞了我好几条答案。

于是我在这里发下：是1536

这里在贴一下部分评測数据，为什么是部分呢？由于是在非常多台电脑上跑的。丢了一些。可是肯定跑全了！

答案是没有错的。

嗯，有好几个数的约数个数都是1536。

额。我还是先贴一下评測代码吧。

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
#define N 15
int ans=0;
int p[N],cnt;
int main()
{
	int i,j,k;
	for(i=1029188160;i<=2000000000;i++)
	{
		cnt=0;
		k=i;
		for(j=2;j*j<=k;j++)
		{
			if(k%j==0)
			{
				p[++cnt]=0;
				while(k%j==0)
				{
					p[cnt]++;
					k/=j;
				}
			}
		}
		if(k>1)p[++cnt]=1;
		int temp=1;
		for(j=1;j<=cnt;j++)
		{
			temp*=(p[j]+1);
		}
		if(ans<temp)
		{
			printf("%d : %d\n",i,ans=temp);
		}
		if(i%10000000==0)printf("%d at %d\n",temp,i);	
	}
	printf("%d\n",ans);
	system("pause");
	return 0;
}

1029188160 : 1344 128 at 1030000000 176 at 1040000000 288 at 1050000000 144 at 1060000000 128 at 1070000000 320 at 1080000000 128 at 1090000000 162 at 1100000000 1102701600 : 1440 256 at 1110000000 192 at 1120000000 128 at 1130000000 288 at 1140000000 144 at 1150000000 160 at 1160000000 384 at 1170000000 144 at 1180000000 256 at 1190000000 198 at 1200000000

1200000000 : 198 198 at 1200000000 1200000528 : 240 1200001440 : 384 1200003840 : 432 1200009600 : 768 1200119760 : 960 1200719520 : 1152 192 at 1210000000 1210809600 : 1296 144 at 1220000000 1225224000 : 1344 256 at 1230000000 1232431200 : 1440 160 at 1240000000 88 at 1250000000 432 at 1260000000 128 at 1270000000 120 at 1280000000 256 at 1290000000 162 at 1300000000

1400000000 : 180 180 at 1400000000 1400000085 : 192 1400000448 : 224 1400000616 : 288 1400001408 : 480 1400011200 : 1008 1401079680 : 1024 1401472800 : 1152 1403438400 : 1260 1409007600 : 1440 256 at 1410000000 144 at 1420000000 256 at 1430000000 288 at 1440000000 144 at 1450000000 144 at 1460000000 384 at 1470000000 1470268800 : 1536 160 at 1480000000 128 at 1490000000 180 at 1500000000

1500000000 : 180 180 at 1500000000 1500000480 : 288 1500001360 : 320 1500001800 : 384 1500003120 : 480 1500004800 : 504 1500012000 : 768 1500127200 : 864 1500206400 : 1008 1500899400 : 1152 1504198080 : 1344 128 at 1510000000 176 at 1520000000 384 at 1530000000 288 at 1540000000 1543782240 : 1440 144 at 1550000000 320 at 1560000000 128 at 1570000000 144 at 1580000000 256 at 1590000000 117 at 1600000000 256 at 1610000000 360 at 1620000000 128 at 1630000000 160 at 1640000000 1643241600 : 1536 288 at 1650000000 144 at 1660000000 128 at 1670000000 352 at 1680000000 192 at 1690000000 162 at 1700000000

1700000000 : 162 162 at 1700000000 1700000064 : 168 1700000120 : 192 1700000610 : 256 1700000640 : 384 1700005440 : 448 1700006000 : 480 1700013600 : 648 1700028000 : 672 1700047440 : 720 1700075520 : 768 1700099280 : 800 1700206200 : 960 1700233920 : 1008 1700899200 : 1152 1706443200 : 1176 1709187480 : 1280 384 at 1710000000 1715313600 : 1512 160 at 1720000000 128 at 1730000000 288 at 1740000000 1745944200 : 1536 160 at 1750000000 192 at 1760000000 256 at 1770000000 144 at 1780000000 128 at 1790000000 270 at 1800000000

1800000000 : 270 270 at 1800000000 1800001500 : 288 1800001632 : 384 1800002160 : 480 1800005760 : 512 1800009120 : 576 1800014400 : 840 1800136800 : 864 1800152640 : 896 1800179640 : 960 1800691200 : 1080 1801079280 : 1280 1807565760 : 1344 128 at 1810000000 1816214400 : 1440 288 at 1820000000 256 at 1830000000 1837836000 : 1536 176 at 1840000000 144 at 1850000000 288 at 1860000000 256 at 1870000000 160 at 1880000000 512 at 1890000000 162 at 1900000000 128 at 1910000000 224 at 1920000000 128 at 1930000000 144 at 1940000000 288 at 1950000000 240 at 1960000000 128 at 1970000000 432 at 1980000000 128 at 1990000000 110 at 2000000000 1536

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