### About the Number 126 (one hundred twenty-six)

MathBabbler created a nBAB for the number 125 on 29 March 2009. While working on that nBAB, he learned that 125 was a Ruth-Aaron pair with `126`. On 31 March 2009, MathBabbler and his CSC100 class wrote a C program that determines if a number is a member of the Ruth-Aaron pair. This nBAB about the number `126` was the second nBAB to use the MBNA's Ruth-Aaron program.

```   MathBabbler Number Analyst (MBNA) output:
=========================================
126 is a natural, whole, integer
126 is even
126 proper divisors are: 1,2,3,6,7,9,14,18,21,42,63,
126 is abundant (sum of divisors is 186)
126 is unhappy
126 is a Harshad number
126 is not prime
126 has the prime factors: 2*3*3*7
126 sum prime factors: 2...3...3...7...answer: 15
126 and 125 are a Ruth-Aaron pair
126 in octal is 0176
126 in hexadecimal is 0x7e
126 in binary is 1111110 (is evil)
126 nearest square numbers: -5...18 (121...144 )
sqrt(126) = 11.225
ln(126) = 4.83628
log(126) = 2.10037
126 reciprocal is .00793650793650793650793650793650
126! is 2.37217e+211
126 is 40.107 Pi years
126 is 6 score and 6 years
126 written as a Roman numeral is CXXVI
```

`[Wikipedia]` `126` is a Friedman number because it is an integer which, in base-10, is the "result of an expression using all its own digits in combination with any of the four basic arithmetic operators and sometimes exponentiation."

```   126 = 6 * 21
```

Observe...

```   sqrt(126) / (ln(126) + log(126)) = 1.6182117
```

1.6182117 minus Phi is 0.000177711762; in other words, the square-root of `126` divided-by the natural log of `126` plus the common log of `126` approximates the Golden Ratio.

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 02 April 2009 