[seqfan] Re: Happy 3³+4³+5³+6³+7³+8³+9³

Giovanni Resta g.resta at iit.cnr.it
Mon Jan 4 09:59:28 CET 2016


Other notable properties of 2016:

(1) The middle value y of the smallest amicable triple, i.e., 3 numbers 
x < y < z such that sigma(x)=sigma(y)=sigma(z) = x+y+z \sigma(n) is the 
sum of the divisors of n.

(2) The only number n such that n^3 + n^2 is strictly pandigital, i.e., 
it contains all the digits 0 to 9 exactly once.

(3) The smallest number equal to the sum of its 31 smallest divisors.

(4) The smallest number whose square root begins with 10 composite 
digits (so 4, 6, 8 or 9).

(5) If p(n) denotes the n-th prime number, the product of digits of 
p(p(666)) is 2016.

(6) T(rev(iT(2016))) = 666, where T(n) is the n-th triangular number, 
rev(n) is the reverse of n, and iT(T(n))=n.

(7) The value of y in this geometrical problem 
http://www.numbersaplenty.com/prob2016.png

Giovanni Resta




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