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 A336177 Numbers k such that there are exactly two powerful numbers between k^2 and (k+1)^2. 5
 5, 11, 14, 22, 25, 33, 44, 46, 55, 58, 62, 70, 72, 73, 82, 88, 96, 98, 103, 104, 109, 110, 111, 124, 129, 135, 155, 156, 158, 164, 172, 176, 178, 181, 187, 197, 203, 206, 207, 209, 212, 218, 240, 243, 248, 249, 254, 257, 259, 268, 277, 279, 281, 285, 288, 291 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Positions of 2's in A119241. Shiu (1980) proved that this sequence has an asymptotic density 0.2312... A more accurate calculation using his formula gives 0.231299167354828... REFERENCES József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, chapter VI, p. 226. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 P. Shiu, On the number of square-full integers between successive squares, Mathematika, Vol. 27, No. 2 (1980), pp. 171-178. EXAMPLE 5 is a term since there are exactly two powerful numbers, 27 = 3^3 and 32 = 2^5 between 5^2 = 25 and (5+1)^2 = 36. MATHEMATICA powQ[n_] := (n == 1) || Min @@ FactorInteger[n][[;; , 2]] > 1; Select[Range[300], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?powQ] == 2 &] CROSSREFS Cf. A001694, A119241, A119242, A336175, A336176, A336178. Sequence in context: A267298 A102801 A314000 * A314001 A196206 A079030 Adjacent sequences:  A336174 A336175 A336176 * A336178 A336179 A336180 KEYWORD nonn AUTHOR Amiram Eldar, Jul 10 2020 STATUS approved

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Last modified July 1 21:41 EDT 2022. Contains 354975 sequences. (Running on oeis4.)