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%I #29 Mar 28 2023 07:59:13
%S 2,5,8,9,10,12,13,16,17,18,20,24,25,26,28,29,31,32,33,34,35,36,37,40,
%T 41,43,44,45,48,50,52,53,54,57,58,59,61,63,64,65,68,72,73,74,76,80,81,
%U 82,85,88,89,90,91,96,97,98,99,100,101,104,106,108,109,112,113,116,117
%N Sum of two powerful numbers (definition (1), A001694).
%C Complement of A085253. - _Reinhard Zumkeller_, Jun 23 2003
%D Aleksandar Ivić, The Riemann Zeta-Function, Wiley, NY, 1985, see p. 439.
%H Amiram Eldar, <a href="/A076871/b076871.txt">Table of n, a(n) for n = 1..10000</a>
%H Valentin Blomer, <a href="http://dx.doi.org/10.1112/S0024610704006040">Binary quadratic forms with large discriminants and sums of two squareful numbers II</a>, Journal of the London Mathematical Society 71:1 (2005), pp. 69-84.
%H Alexander Kalmynin and Segei Konyagin, <a href="https://arxiv.org/abs/2303.14833">Large gaps between sums of two squareful numbers</a>, arXiv:2303.14833 [math.NT], 2023.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerfulNumber.html">Powerful Number</a>.
%F A085252(a(n)) > 0. - _Reinhard Zumkeller_, Jun 23 2003
%F Blomer shows that there are x/log^k x sums of two powerful numbers up to x, where k = 0.20629947... is A261883. - _Charles R Greathouse IV_, Sep 04 2015
%t With[{m = 120}, pow = Select[Range[m], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]; Select[Union[Plus @@@ Tuples[pow, {2}]], # <= m &]] (* _Amiram Eldar_, Jan 30 2023 *)
%Y Cf. A001694, A076872, A085252, A085253, A261883.
%Y Different from A070049.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Nov 25 2002
%E More terms from _Vladeta Jovovic_, Nov 25 2002
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