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.

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1 comment:

  1. AnonymousAugust 20, 2010 at 5:18 AM

    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
    see http://sites.Google.com/site/Numeropedia
    81=2^6+17=2^3+73=2^5+7^2=2^9-431=10^2-19=2^15-32687
    81 may be represented as a Pythagorean triple
    81^2+3280^2=3281^2
    Rafael Parra Machio

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