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 A282570 #7 Feb 16 2025 08:33:41
%S A282570 0,0,1,0,0,0,0,2,0,2,0,2,1,0,2,2,5,0,2,0,3,2,4,4,2,2,0,4,5,4,3,2,4,2,
%T A282570 4,6,8,4,0,4,6,8,5,6,5,4,2,8,10,8,2,0,7,6,7,4,8,4,2,8,10,12,2,6,4,10,
%U A282570 9,6,9,4,7,6,14,12,2,6,5,10,7,10,8,4,4,10,14,8,6,6,10,8,10,12,15,8,6,14
%N A282570 Number of ways to write n as an ordered sum of two multiplicatively perfect numbers (A007422).
%C A282570 Conjecture: a(n) > 0 for all n > 51.
%H A282570 Ilya Gutkovskiy, <a href="/A282570/a282570.pdf">Extended graphical example</a>
%H A282570 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiplicativePerfectNumber.html">Multiplicative Perfect Number</a>
%F A282570 G.f.: (Sum_{k>=1} x^A007422(k))^2.
%e A282570 a(16) = 5 because we have [15, 1], [10, 6], [8, 8], [6, 10] and [1, 15].
%t A282570 nmax = 95; CoefficientList[Series[Sum[Boole[Sqrt[k]^DivisorSigma[0, k]/k == k] x^k, {k, 1, nmax}]^2, {x, 0, nmax}], x]
%Y A282570 Cf. A007422, A236473, A280683, A282569.
%K A282570 nonn
%O A282570 0,8
%A A282570 _Ilya Gutkovskiy_, Feb 18 2017