Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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