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%I #9 Jul 18 2020 04:33:04
%S 2,8,10,15,16,18,19,20,28,29,37,39,41,42,45,48,50,51,52,53,56,57,59,
%T 63,65,74,76,77,78,79,83,84,87,89,90,92,94,100,101,102,107,113,114,
%U 115,116,117,118,119,121,122,126,127,130,134,138,141,144,146,147,148
%N Numbers k such that there is a single powerful number between k^2 and (k+1)^2.
%C Positions of 1's in A119241.
%C Shiu (1980) proved that this sequence has an asymptotic density 0.3955... A more accurate calculation using his formula gives 0.3955652153962362...
%C 1 is the most common value of A119241.
%D József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, chapter VI, p. 226.
%H Amiram Eldar, <a href="/A336176/b336176.txt">Table of n, a(n) for n = 1..10000</a>
%H P. Shiu, <a href="https://doi.org/10.1112/S0025579300010056">On the number of square-full integers between successive squares</a>, Mathematika, Vol. 27, No. 2 (1980), pp. 171-178.
%e 2 is a term since there is a single powerful number, 8 = 2^3, between 2^2 = 4 and (2+1)^2 = 9.
%t powQ[n_] := (n == 1) || Min @@ FactorInteger[n][[;; , 2]] > 1; Select[Range[150], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?powQ] == 1 &]
%Y Cf. A001694, A119241, A119242, A336175, A336177, A336178.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jul 10 2020