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 A280683 #16 Feb 16 2025 08:33:39
%S A280683 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,0,0,3,2,0,0,2,2,0,2,3,2,1,2,4,0,0,
%T A280683 2,6,2,0,2,4,4,1,4,5,4,0,4,8,6,2,0,5,4,4,4,6,4,0,4,8,10,0,2,4,6,3,6,9,
%U A280683 4,3,6,14,8,2,4,5,8,3,10,8,4,0,8,12,4,4,4,8,6,8,12,11,6,2,10,12,12,4,8,12,12,5,12,10,4,6
%N A280683 Number of ways to write n as an ordered sum of two positive squarefree semiprimes (A006881).
%C A280683 Conjecture: a(n) > 0 for n > 82 (see comment in A006881 from _Richard R. Forberg_).
%H A280683 Ilya Gutkovskiy, <a href="/A280683/a280683.pdf">Extended graphical example</a>
%H A280683 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime</a>
%H A280683 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Squarefree.html">Squarefree</a>
%F A280683 G.f.: (Sum_{k>=2} mu(k)^2*floor(bigomega(k)/2)*floor(2/bigomega(k))*x^k)^2, where mu(k) is the Moebius function (A008683) and bigomega(k) is the number of prime divisors of k counted with multiplicity (A001222).
%F A280683 a(n) = Sum_{k=1..n-1} c(k) * c(n-k), where c = A280710. - _Wesley Ivan Hurt_, Jan 07 2024
%e A280683 a(20) = 3 because we have [14, 6], [10, 10] and [6, 14].
%t A280683 nmax = 106; Rest[CoefficientList[Series[(Sum[MoebiusMu[k]^2 Floor[PrimeOmega[k]/2] Floor[2/PrimeOmega[k]] x^k, {k, 2, nmax}])^2, {x, 0, nmax}], x]]
%Y A280683 Cf. A001222, A001358, A005117, A006881, A008683, A073610, A098235, A199331, A280710.
%K A280683 nonn,easy
%O A280683 1,16
%A A280683 _Ilya Gutkovskiy_, Jan 07 2017