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%I #18 May 14 2017 00:01:26
%S 1,1,1,1,2,2,2,2,4,5,5,5,7,8,8,8,12,14,15,15,19,21,22,22,28,33,35,37,
%T 43,48,50,52,62,70,75,79,92,100,105,109,126,140,148,157,177,194,202,
%U 211,237,261,276,290,324,351,370,384,424,462,489,514,562,609,640,670,728,787,831,873,948,1016,1071,1118,1210,1296,1366,1433
%N Number of partitions of n into powerful parts (A001694).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerfulNumber.html">Powerful Number</a>
%H <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F G.f.: Product_{k>=1} 1/(1 - x^A001694(k)).
%F a(n) = A078635(n) for n < 72.
%e a(8) = 4 because we have [8], [4, 4], [4, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1].
%t nmax = 75; CoefficientList[Series[1/(1 - x) Product[1/(1 - Boole[Min@ FactorInteger[k][[All, 2]] > 1] x^k), {k, 2, nmax}], {x, 0, nmax}], x]
%Y Cf. A001694, A078635, A286320.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, May 12 2017
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