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 360,360 is the smallest number that has 1-13, 1-14 and 1-15 as proper divisors. The sum of the proper divisors for 360,360 is

1,212,120.MathBabbler Number Analyst (MBNA) output: ========================================= 1212120 is a natural, whole, integer 1212120 is even 1212120 proper divisors are: 1,2,3,4,5,6,7,8,9,10,12,13,14,15,18,20,21,24,26, 28,30,35,36,37,39,40,42,45,52,56,60,63,65,70,72, 74,78,84,90,91,104,105,111,117,120,126,130,140, 148,156,168,180,182,185,195,210,222,234,252,259, 260,273,280,296,312,315,333,360,364,370,390,420, 444,455,468,481,504,518,520,546,555,585,630,666, 728,740,777,780,819,840,888,910,936,962,1036,1092, 1110,1170,1260,1295,1332,1365,1443,1480,1554,1560, 1638,1665,1820,1924,2072,2184,2220,2331,2340,2405, 2520,2590,2664,2730,2886,3108,3276,3330,3367,3640, 3848,3885,4095,4329,4440,4662,4680,4810,5180,5460, 5772,6216,6552,6660,6734,7215,7770,8190,8658,9324, 9620,10101,10360,10920,11544,11655,13320,13468, 14430,15540,16380,16835,17316,18648,19240,20202, 21645,23310,26936,28860,30303,31080,32760,33670, 34632,40404,43290,46620,50505,57720,60606,67340, 80808,86580,93240,101010,121212,134680,151515, 173160,202020,242424,303030,404040,606060, 1212120 has 191 proper divisors 1212120 is abundant (sum of divisors is 3767400; ratio: 3.10811) 1212120 is unhappy 1212120 is a Harshad number 1212120 is not prime 1212120 has the prime factors: 2*2*2*3*3*5*7*13*37 (sum=74) 2...2...2...3...3...5...7...13...37...answer: 74 1212120 in octal is 04477330 1212120 in hexadecimal is 0x127ed8 1212120 in binary is 100100111111011011000 (is evil) 1212120 nearest square numbers: -2120...81 (1210000...1212201 [1101]) sqrt(1212120) = 1100.96 ln(1212120) = 14.0079 log(1212120) = 6.08355 1212120 reciprocal is .00000082500082500082500082500082 1212120 is an apocalyptic power 1212120! is inf 1.21212e+06 is 385830 Pi years 1.21212e+06 is 60606 scoreyears 1212120 = 303031^2 - 303029^2 and 2 * (303031 + 303029) = 1212120

**Creator:** Gerald Thurman
[gthurman@gmail.com]

**Created:** 22 November 2013 (posted 25 November 2013)

This work is licensed under a Creative Commons Attribution 3.0 United States License.