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%I #11 Dec 26 2012 14:45:35
%S 3,17,33,41,66,77,89,117,133,145,153,189,161,225,301,257,324,333,341,
%T 297,432,425,369,517,613,441,521,585,513,809,689,792,657,1001,801,881,
%U 1000,1017,873,945,900,1265,1169,1425,1089,1125,1197,1481,1161,1584
%N a(n) is the smallest number representable in exactly n ways as a sum of 3 powerful(1) numbers.
%C Here we are considering powerful numbers (first definition) A001694. Note that, by definition, 1 is powerful.
%H Donovan Johnson, <a href="/A115355/b115355.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerfulNumber.html">Powerful Number.</a>
%e a(2) = 17 since 17 = 4+4+9 = 8+8+1.
%t pwfQ[n_] := n==1 || Min[Transpose[FactorInteger@n][[2]]] > 1; lim = 5000; pt = Select[Range[lim], pwfQ]; t = Table[0, {i, lim}]; Do[v = pt[[i]]+pt[[j]]+pt[[k]]; If[v <= lim, t[[v]]++ ], {i, Length@pt}, {j, i}, {k, j}]; Table[Position[t, k][[1, 1]], {k, 60}]
%Y Cf. A001694, A085252, A085253, A085254, A085255, A063274, A115354.
%K nonn
%O 1,1
%A _Giovanni Resta_, Jan 21 2006