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Expansion of (Sum_{k>=2} floor(1/omega(k))*x^k)^2, where omega(k) is the number of distinct prime factors (A001221).
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%I #7 Apr 23 2017 23:59:15

%S 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 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 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 Expansion of (Sum_{k>=2} floor(1/omega(k))*x^k)^2, where omega(k) is the number of distinct prime factors (A001221).

%C Number of ordered ways of writing n as the sum of two prime powers (1 excluded).

%H G. C. Greubel, <a href="/A280242/b280242.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimePower.html">Prime Power</a>

%F G.f.: (Sum_{k>=2} floor(1/omega(k))*x^k)^2.

%e a(6) = 3 because we have [4, 2], [3, 3] and [2, 4].

%t nmax = 97; CoefficientList[Series[(Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}])^2, {x, 0, nmax}], x]

%Y Cf. A001221, A071330, A071331, A073610, A095840, A246655.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Dec 29 2016