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 A363967 #11 Apr 27 2025 03:22:57
%S A363967 1,3,9,22,27,30,40,63,66,70,81,88,90,94,115,119,120,138,153,156,170,
%T A363967 171,174,184,189,190,198,210,214,217,232,264,265,270,280,282,310,318,
%U A363967 322,323,343,345,357,360,364,376,382,385,399,400,414,416,462,468,472,495,497
%N A363967 Numbers whose divisors can be partitioned into two disjoint sets whose both sums are squares.
%C A363967 If one of the two sets is empty then the term is a number whose sum of divisors is a square (A006532).
%C A363967 If k is a number such that (6*k)^2 is the sum of a twin prime pair (A037073), then (18*k^2)^2 - 1 is a term.
%C A363967 3 is the only prime term.
%H A363967 Amiram Eldar, <a href="/A363967/b363967.txt">Table of n, a(n) for n = 1..10000</a>
%e A363967 9 is a term since its divisors, {1, 3, 9}, can be partitioned into the two disjoint sets, {1, 3} and {9}, whose sums, 1 + 3 = 4 = 2^2 and 9 = 3^2, are both squares.
%t A363967 sqQ[n_] := IntegerQ[Sqrt[n]]; q[n_] := Module[{d = Divisors[n], s, p}, s = Total[d]; p = Position[Rest @ CoefficientList[Product[1 + x^i, {i, d}], x], _?(# > 0 &)] // Flatten; AnyTrue[p, sqQ[#] && sqQ[s - #] &]]; Select[Range[500], q]
%Y A363967 Cf. A000203, A000290, A037073.
%Y A363967 Subsequence of A333911.
%Y A363967 A006532 is a subsequence.
%Y A363967 Similar sequences: A333677, A360694.
%K A363967 nonn
%O A363967 1,2
%A A363967 _Amiram Eldar_, Jun 30 2023