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 A294739 #21 Feb 16 2025 08:33:51
%S A294739 53,56,59,61,64,67,68,74,79,93,95,96,102,111,114,153,177
%N A294739 Numbers that are the sum of 5 nonzero squares in exactly 5 ways.
%C A294739 Theorem: There are no further terms. Proof (from a proof by _David A. Corneth_ on Nov 08 2017 in A294736): The von Eitzen link states that if n > 5408 then the number of ways to write n as a sum of 5 squares is at least floor(sqrt(n - 101) / 8) = 9. For n <= 5408, terms have been verified by inspection. Hence this sequence is finite and complete.
%D A294739 E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.
%H A294739 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 A294739 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.
%H A294739 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SquareNumber.html">Square Number.</a>
%H A294739 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%t A294739 fQ[n_] := Block[{pr = PowersRepresentations[n, 5, 2]}, Length@ Select[pr, #[[1]] > 0 &] == 5]; Select[ Range@ 200, fQ] (* _Robert G. Wilson v_, Nov 17 2017 *)
%Y A294739 Cf. A025429, A025357, A294675, A294736.
%K A294739 nonn,fini,full
%O A294739 1,1
%A A294739 _Robert Price_, Nov 07 2017