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 A385963 #18 Jul 18 2025 19:50:53
%S A385963 0,1,1,1,1,2,1,3,1,4,5,5,5,6,7,7,7,8,8,9,9,9,9,11,10,11,11,11,11,11,
%T A385963 13,12,12,13,14,13,14,14,15,15,15,16,16,16,16,17,17,17,18,18,18,18,19,
%U A385963 19,19,19,19,19,19,20,21,21,21,21,22,22,22,22,23,22,24,24,24,24,24,25
%N A385963 a(n) is the maximum number of distinct positive integers whose sum of squares is equal to n^2.
%C A385963 An upper bound is a(n) <= r for the largest r with 1^2 + ... + r^2 <= n^2, and with equality only at n = 0,1,24, the latter being a(70) = 24 (see comments A001032).
%H A385963 David A. Corneth, <a href="/A385963/b385963.txt">Table of n, a(n) for n = 0..10000</a>
%H A385963 David A. Corneth, <a href="/A385963/a385963_1.gp.txt">n, a(n), one tuple of size a(n) where sum of elements of tuples is n^2</a>
%e A385963 For n = 11, there are A030273(11) = 4 partitions of 11^2 into distinct squares: {11^2}, {2^2, 6^2, 9^2}, {1^2, 2^2, 4^2, 10^2}, {1^2, 2^2, 4^2, 6^2, 8^2}, where the largest cardinality of these sets is 5. Therefore, a(11) = 5.
%o A385963 (PARI) a(n)=poldegree(polcoef(prod(k=1, n, 1 + y*x^(k^2), 1 + O(x^(n^2+1))), n^2)) \\ _Andrew Howroyd_, Jul 13 2025
%Y A385963 Cf. A030273, A001032.
%K A385963 nonn
%O A385963 0,6
%A A385963 _Gonzalo MartÃnez_, Jul 13 2025
%E A385963 More terms from _Andrew Howroyd_, Jul 13 2025