About the Number 145 (one hundred forty-five)

This nBAB for 145 was created because MathBabbler was in the mood to create a nBAB and 145 was the smallest number without a nBAB.

   MathBabbler Number Analyst (MBNA) output:
   =========================================
   145 is a natural, whole, integer
   145 is odd
   145 proper divisors are: 1,5,29,
   145 is deficient (sum of divisors is 35)
   145 is unhappy
   145 is not a Harshad number
   145 is not prime
   145 has the prime factors: 5*29 (sum=34)
   145 is semiprime (biprime or 2-almost prime)
   145 sum of prime factors is: 34
   145 is ThurmNumber
   145 is a Leyland number (3^4+4^3)
   145 in octal is 0221
   145 in hexadecimal is 0x91
   145 in binary is 10010001 (is odious)
   145 nearest square numbers: -1...24 (144...169 [13])
   sqrt(145) = 12.0416
   ln(145) = 4.97673
   log(145) = 2.16137
   145 reciprocal is .00689655172413793103448275862068
   145! is 8.04793e+251
   145 is 46.1549 Pi years
   145 is 7 score and 5 years
   145 written as a Roman numeral is CXLV
   145 = 73^2 - 72^2 and 73 + 72 = 145

NumberGossip.com reported that "145 is the smallest number (besides the trivial cases of 1 and 2) that is the sum of the factorials of its digits (1!+4!+5!).

NumDic.com reported that 145 is a pentagonal number and that it is the sum of two squares (9^2+8^2).

OEIS.org::id:A000326.

   Pentagonal numbers: n(3n-1)/2 

   0, 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 
   247, 287, 330, 376, 425, 477, 532, 590, 651, 715, 782, 
   852, 925, 1001, 1080, 1162, 1247, 1335, 1426, 1520, 
   1617, 1717, 1820, 1926, 2035, 2147, ...

   n is a pentagonal number if...  (sqrt(24n+1) + 1)/6 
   evaluates to a whole number

The creation of this nBAB for the number 145 prompted MathBabbler to write this C++ program that checks if a number is a pentagonal number. This program has been added to the MBNA (MathBabbler Number Analyst).


Creator: Gerald Thurman [gthurman@gmail.com]
Created: 11 March 2010

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