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 A280242 #8 Feb 16 2025 08:33:38
%S A280242 0,0,0,0,1,2,3,4,3,4,5,6,6,6,5,6,7,4,7,6,8,8,7,4,8,6,7,8,8,6,10,6,11,
%T A280242 8,13,8,14,4,9,8,12,6,10,6,10,10,11,4,14,6,13,8,12,4,15,6,14,8,11,4,
%U A280242 14,6,11,8,13,4,18,4,14,10,14,4,18,6,13,12,14,6,18,4,16,8,11,8,20,6,17,8,14,6,22,8,16,6,13,4,20,4
%N A280242 Expansion of (Sum_{k>=2} floor(1/omega(k))*x^k)^2, where omega(k) is the number of distinct prime factors (A001221).
%C A280242 Number of ordered ways of writing n as the sum of two prime powers (1 excluded).
%H A280242 G. C. Greubel, <a href="/A280242/b280242.txt">Table of n, a(n) for n = 0..1000</a>
%H A280242 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimePower.html">Prime Power</a>
%F A280242 G.f.: (Sum_{k>=2} floor(1/omega(k))*x^k)^2.
%e A280242 a(6) = 3 because we have [4, 2], [3, 3] and [2, 4].
%t A280242 nmax = 97; CoefficientList[Series[(Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}])^2, {x, 0, nmax}], x]
%Y A280242 Cf. A001221, A071330, A071331, A073610, A095840, A246655.
%K A280242 nonn
%O A280242 0,6
%A A280242 _Ilya Gutkovskiy_, Dec 29 2016