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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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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