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%I #7 Apr 23 2017 23:59:21
%S 0,0,0,0,0,0,1,3,6,10,12,15,19,24,30,34,36,39,45,45,51,52,57,66,67,66,
%T 69,73,75,87,81,87,93,94,99,111,111,126,129,130,123,141,126,156,138,
%U 150,132,168,145,168,153,172,165,195,156,189,171,202,177,228,165,225,183,225,186,243,177,243,204,238,198
%N Expansion of (Sum_{k>=2} floor(1/omega(k))*x^k)^3, where omega(k) is the number of distinct prime factors (A001221).
%C Number of ordered ways of writing n as sum of three prime powers (1 excluded).
%H G. C. Greubel, <a href="/A280243/b280243.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)^3.
%e a(7) = 3 because we have [3, 2, 2], [2, 3, 2] and [2, 2, 3].
%t nmax = 70; CoefficientList[Series[(Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}])^3, {x, 0, nmax}], x]
%Y Cf. A001221, A098238, A246655.
%K nonn
%O 0,8
%A _Ilya Gutkovskiy_, Dec 29 2016
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