### About the Number 720720 (seven hundred twenty thousand seven hundred twenty)

MathBabbler learned that the number 2520 was the smallest number that had the number 1 through 10 as proper divisors. A progam was writte to print the smallest numbers that have proper divisors 1-3, 1-4, 1-5, and so on to 1-24. The number 720,720 is the smallest number that has 1-16 as proper divisors.

```MathBabbler Number Analyst (MBNA) output:
=========================================
720720 is a natural, whole, integer
720720 is even
720720 proper divisors are: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,
20,21,22,24,26,28,30,33,35,36,39,40,42,44,
45,48,52,55,56,60,63,65,66,70,72,77,78,80,
84,88,90,91,99,104,105,110,112,117,120,126,
130,132,140,143,144,154,156,165,168,176,180,
182,195,198,208,210,220,231,234,240,252,260,
264,273,280,286,308,312,315,330,336,360,364,
385,390,396,420,429,440,455,462,468,495,504,
520,528,546,560,572,585,616,624,630,660,693,
715,720,728,770,780,792,819,840,858,880,910,
924,936,990,1001,1008,1040,1092,1144,1155,1170,
1232,1260,1287,1320,1365,1386,1430,1456,1540,1560,
1584,1638,1680,1716,1820,1848,1872,1980,2002,2145,
2184,2288,2310,2340,2520,2574,2640,2730,2772,2860,
3003,3080,3120,3276,3432,3465,3640,3696,3960,4004,
4095,4290,4368,4620,4680,5005,5040,5148,5460,5544,
5720,6006,6160,6435,6552,6864,6930,7280,7920,8008,
8190,8580,9009,9240,9360,10010,10296,10920,11088,
11440,12012,12870,13104,13860,15015,16016,16380,
17160,18018,18480,20020,20592,21840,24024,25740,
27720,30030,32760,34320,36036,40040,45045,48048,
51480,55440,60060,65520,72072,80080,90090,102960,
120120,144144,180180,240240,360360,
720720 is refactorable (evenly divisable  by # of divisors)
720720 has 239 proper divisors
720720 is abundant (sum of divisors is 2529072; ratio: 3.50909)
720720 is unhappy
720720 is not prime
720720 has the prime factors: 2*2*2*2*3*3*5*7*11*13 (sum=50)
720720 in octal is 02577520
720720 in binary is 10101111111101010000 (is evil)
720720 nearest square numbers: -1616...81 (719104...720801 [849])
sqrt(720720) = 848.952
ln(720720) = 13.488
log(720720) = 5.85777
720720 reciprocal is .00000138750138750138750138750138
720720 is an apocalyptic power
720720! is inf
720720 is 229412 Pi years
720720 is 36036 scoreyears
720720 = 180181^2 - 180179^2 and 2 * (180181 + 180179) = 720720
```

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 23 November 2013 (posted 25 November 2013)