%I #11 Dec 10 2012 16:00:49
%S 2,17,108,153,297,657,1764,2052,4644,6156,10800,16200,22932,29000,
%T 11025,54225,92025,68796,100548,99225,44100,88200,264600,431244,
%U 176400,441000,666468,1151172,352800,617400,396900,926100,980100,793800,1234800
%N a(n) is the smallest number representable in exactly n ways as a sum of 2 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="/A115354/b115354.txt">Table of n, a(n) for n = 1..120</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 = 16+1 = 8+9.
%t pwfQ[n_] := n == 1 || Min[Transpose[FactorInteger@n][[2]]] > 1; lim=200000; pt = Select[Range[lim], pwfQ]; t = Table[0, {i, lim}]; Do[v = pt[[i]]+ pt[[j]]; If[v<=lim, t[[v]]++ ], {i, Length@pt}, {j, i}]; Table[Position[t, k][[1, 1]], {k, 22}]
%Y Cf. A001694, A085252, A085253, A085254, A085255, A063274, A115355.
%K nonn
%O 1,1
%A _Giovanni Resta_, Jan 21 2006
%E a(23)-a(35) from _Donovan Johnson_, Dec 07 2008