## Wednesday, August 18, 2010

### 81

81 = 34, a perfect fourth power.

81 is the only integer other than 1 that is the square of the sum of its digits.

81 is a centered octagonal number.

81 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 (the first nine odd numbers).

The chemical element thallium has the atomic number 81.

#### 1 comment:

Anonymous said...

Other features of the number 81:
81 is a perfect number by the totient, Q (n) as
Q(81)=54,Q(54)=18,Q(18)=6,Q(6)=2,Q(2)=1 and 54+18+6+2+1 =81, see A082897
Tribonacci 81 is a number, since (n-1)+(n-2)+(n-3)=81 with n=29
81 is a Harshad number, as 81/(8+1)=9
81 Meander, number of ways you can cross a road to a river n times, see A005316
81 is the tenth number of the Mian-Chowla sequence as
1+(4+5+6)+(11+12+13+14+15)=3^4=81, see A005282 and also
http://Mathworl.Wolfram.com/Mian-ChowlaSequebce/
81 also can be represented as
81=41+40=41^2-40^2
81=1^2+4^2+8^2
81=(1+2+2+4)^2=1^3+2^3+2^3+4^3
81=5+6+7+8+9+10+11+12+13
81=(1+2)^4=[(1^5+2^5)+(1+2^7)]/2
81^3=531441=(5+31+44+1)^3
81^4=43046721=(4+3+0+46+7+21)^4