login
Numbers that have exactly three representations as a sum of seven positive squares.
0

%I #10 Dec 03 2017 00:43:09

%S 31,34,39,43,47,51,56,59,68

%N Numbers that have exactly three representations as a sum of seven positive squares.

%C It appears that this sequence is finite and complete. See the von Eitzen link for a proof for the 5 positive squares case.

%D E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.

%H H. von Eitzen, in reply to user James47, <a href="http://math.stackexchange.com/questions/811824/what-is-the-largest-integer-with-only-one-representation-as-a-sum-of-five-nonzer">What is the largest integer with only one representation as a sum of five nonzero squares?</a> on stackexchange.com, May 2014

%H D. H. Lehmer, <a href="http://www.jstor.org/stable/2305380">On the Partition of Numbers into Squares</a>, The American Mathematical Monthly, Vol. 55, No. 8, October 1948, pp. 476-481.

%Y Cf. A025431, A287166, A295693.

%K nonn,more

%O 1,1

%A _Robert Price_, Nov 27 2017