OFFSET
1,1
COMMENTS
The Heronian mean of two nonnegative real numbers x and y is (x + y + sqrt(xy))/3. Therefore any number n is the Heronian mean of x = 3n and y = 0 (and also of x = n and y = n).
In particular, the sequence contains all numbers n = 3k which equal three times the Heronian mean of k and itself. If the two integers are required to be distinct then most multiples of 3 are no longer in the sequence: see A050931 for the sequence of integers that equal the Heronian mean of two distinct positive integers. Writing x = r^2*s where s is squarefree, the square root is an integer iff y = k^2*s for some integer k, and thus n = s*(r^2 + k^2 + rk). Therefore this sequence consists of the numbers listed in A024614 and their multiples by squarefree s. - M. F. Hasler, Aug 17 2016
LINKS
Eric W. Weisstein, Heronian Mean. From MathWorld--A Wolfram Web Resource.
Wikipedia, Heronian mean
EXAMPLE
35 is in the sequence since 5 + 20 + sqrt(5*20) = 35.
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Pahikkala Jussi, Feb 17 2008
EXTENSIONS
Edited and definition corrected, following a remark by Robert Israel, by M. F. Hasler, Aug 17 2016
STATUS
approved