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 A338392 Numbers k such that there are exactly five biquadratefree powerful numbers (A338325) between k^2 and (k+1)^2. 5
 3510, 3611, 16871, 25076, 26910, 35810, 50501, 83107, 101287, 104686, 111836, 152924, 153433, 217983, 239163, 247301, 262413, 266282, 277635, 294453, 298950, 340228, 344510, 362830, 369877, 385336, 475063, 524827, 536793, 537713, 539293, 567062, 568609, 614283 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Positions of 5's in A338326. The asymptotic density of this sequence is 0.000011113... (Dehkordi, 1998). LINKS Massoud H. Dehkordi, Asymptotic formulae for some arithmetic functions in number theory, Ph.D. thesis, Loughborough University, 1998. EXAMPLE 3510 is a term since there are exactly five biquadratefree powerful numbers, 12320648 = 2^3 * 17^2 * 73^2, 12321000 = 2^3 * 3^2 * 5^3 * 37^2, 12324500 = 2^2 * 5^3 * 157^2, 12325975 = 5^2 * 79^3 and 12326391 = 3^3 * 7^3 * 11^3, between 3510^2 = 12320100 and (3510+1)^2 = 12327121. MATHEMATICA bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[25000], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?bqfpowQ] == 5 &] CROSSREFS Cf. A338325, A338326, A338327, A338387, A338388, A338389, A338390, A338391. Sequence in context: A338978 A274237 A053804 * A342399 A043448 A281002 Adjacent sequences:  A338389 A338390 A338391 * A338393 A338394 A338395 KEYWORD nonn AUTHOR Amiram Eldar, Oct 23 2020 STATUS approved

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Last modified May 6 17:00 EDT 2021. Contains 343586 sequences. (Running on oeis4.)