This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A295150 #15 Feb 26 2019 08:07:20 %S A295150 4,5,8,9,10,11,12,14,23,24 %N A295150 Numbers that have exactly two representations as a sum of five nonnegative squares. %C A295150 This sequence is finite and complete. See the von Eitzen Link and the proof in A294675 stating that for n > 5408, the number of ways to write n as a sum of 5 squares (without allowing zero squares) is at least floor(sqrt(n - 101) / 8) = 9. Since this sequence relaxes the restriction of zero squares, the number of representations for n > 5408 is at least nine. Then an inspection of n <= 5408 completes the proof. %D A295150 E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1. %H A295150 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 A295150 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. %t A295150 okQ[n_] := Length[PowersRepresentations[n, 5, 2]] == 2; %t A295150 Select[Range[100], okQ] (* _Jean-François Alcover_, Feb 26 2019 *) %Y A295150 Cf. A000174, A006431, A294675. %K A295150 nonn,fini,full %O A295150 1,1 %A A295150 _Robert Price_, Nov 15 2017