%I #13 Jan 30 2023 02:35:36
%S 0,1,0,0,1,0,0,1,1,1,0,1,1,0,0,1,2,1,0,1,0,0,0,1,1,1,0,1,1,0,1,1,2,1,
%T 1,2,1,0,0,2,2,0,1,1,1,0,0,1,0,2,0,2,1,1,0,0,2,1,1,0,1,0,1,1,2,0,0,2,
%U 0,0,0,2,2,1,0,2,0,0,0,2,2,1,0,0,2,0,0,1,2,1,1,0,0,0,0,1,2,1,1,1,1,0
%N Number of ways to write n as sum of two powerful numbers (A001694).
%H Amiram Eldar, <a href="/A085252/b085252.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerfulNumber.html">Powerful Number</a>.
%F a(A085253(n)) = 0.
%F a(A076871(n)) > 0.
%F a(A085254(n)) = 1.
%F a(A085255(n)) > 1.
%e a(81) = 2: 81 = 9 + 72 = A001694(4) + A001694(12) = 32 + 49 = A001694(8) + A001694(10).
%t With[{m = 120}, pow = Select[Range[m], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]; BinCounts[Select[Plus @@@ Union[Sort /@ Tuples[pow, {2}]], # <= m &], {1, m, 1}]] (* _Amiram Eldar_, Jan 30 2023 *)
%Y Cf. A001694, A076871, A085253, A085254, A085255.
%K nonn
%O 1,17
%A _Reinhard Zumkeller_, Jun 23 2003