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 A282289 #9 Feb 16 2025 08:33:41
%S A282289 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,4,0,0,6,12,6,0,8,12,12,4,
%T A282289 13,16,6,4,13,28,12,4,10,24,24,16,28,24,24,24,42,52,18,28,32,60,40,24,
%U A282289 44,28,42,28,60,52,18,24,37,84,54,48,42,60,78,48,72,44,60,52,68,96,36,40,22,72,72,52,76,52,66,36,88,88,64,56
%N A282289 Expansion of (Sum_{p prime, k>=2} x^(p^k))^4.
%C A282289 Number of ways to write n as an ordered sum of 4 proper prime powers (A246547).
%C A282289 Conjecture: a(n) > 0 for all n > 27.
%H A282289 Ilya Gutkovskiy, <a href="/A282289/a282289.pdf">Extended graphical example</a>
%H A282289 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimePower.html">Prime Power</a>
%F A282289 G.f.: (Sum_{p prime, k>=2} x^(p^k))^4.
%e A282289 a(28) = 8 because we have [16, 4, 4, 4], [8, 8, 8, 4], [8, 8, 4, 8], [8, 4, 8, 8], [4, 16, 4, 4], [4, 8, 8, 8], [4, 4, 16, 4] and [4, 4, 4, 16].
%t A282289 nmax = 91; CoefficientList[Series[Sum[Sign[PrimeOmega[k] - 1] Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}]^4, {x, 0, nmax}], x]
%Y A282289 Cf. A246547, A280242, A280243, A282062, A282064.
%K A282289 nonn
%O A282289 0,21
%A A282289 _Ilya Gutkovskiy_, Feb 11 2017