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 A338391 Numbers k such that there are exactly four biquadratefree powerful numbers (A338325) between k^2 and (k+1)^2. 6
 234, 675, 2426, 8075, 8391, 9093, 9548, 10214, 10340, 11213, 13816, 14523, 14970, 15593, 17329, 17803, 20649, 22483, 23020, 23128, 24842, 25971, 26318, 26557, 28241, 28677, 29124, 29837, 31058, 31338, 31732, 31907, 32490, 35676, 35765, 36302, 37599, 41077, 42577 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Positions of 4's in A338326. The asymptotic density of this sequence is 0.000089634... (Dehkordi, 1998). LINKS Amiram Eldar, Table of n, a(n) for n = 1..600 Massoud H. Dehkordi, Asymptotic formulae for some arithmetic functions in number theory, Ph.D. thesis, Loughborough University, 1998. EXAMPLE 234 is a term since there are exactly four biquadratefree powerful numbers, 54872 = 2^3 * 19^3, 54925 = 5^2 * 13^3, 55112 = 2^3 * 83^2 and 55125 = 3^2 * 5^3 * 7^2, between 234^2 = 54756 and (234+1)^2 = 55225. MATHEMATICA bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[10^4], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?bqfpowQ] == 4 &] CROSSREFS Cf. A338325, A338326, A338327, A338387, A338388, A338389, A338390, A338392. Sequence in context: A256086 A186897 A184450 * A304615 A287878 A252338 Adjacent sequences:  A338388 A338389 A338390 * A338392 A338393 A338394 KEYWORD nonn AUTHOR Amiram Eldar, Oct 23 2020 STATUS approved

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Last modified May 16 03:46 EDT 2021. Contains 343937 sequences. (Running on oeis4.)