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A338388 Numbers k such that there is a single biquadratefree powerful number (A338325) between k^2 and (k+1)^2. 7

%I

%S 2,5,8,10,11,18,19,22,25,33,37,42,46,48,51,52,53,55,57,58,59,65,70,73,

%T 78,87,88,92,94,96,102,103,104,109,111,114,115,116,119,121,122,135,

%U 144,145,149,150,155,157,164,165,166,176,181,182,183,185,190,191,195

%N Numbers k such that there is a single biquadratefree powerful number (A338325) between k^2 and (k+1)^2.

%C Positions of 1's in A338326.

%C The asymptotic density of this sequence is 0.308276695... (Dehkordi, 1998).

%H Amiram Eldar, <a href="/A338388/b338388.txt">Table of n, a(n) for n = 1..10000</a>

%H Massoud H. Dehkordi, <a href="https://hdl.handle.net/2134/12177">Asymptotic formulae for some arithmetic functions in number theory</a>, Ph.D. thesis, Loughborough University, 1998.

%e 2 is a term since there is a single biquadratefree powerful number, 8 = 2^3, between 2^2 = 4 and (2+1)^2 = 9.

%t bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[200], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?bqfpowQ] == 1 &]

%Y Cf. A336176, A338325, A338326, A338327, A338387, A338389, A338390, A338391, A338392.

%K nonn

%O 1,1

%A _Amiram Eldar_, Oct 23 2020

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Last modified July 24 16:24 EDT 2021. Contains 346273 sequences. (Running on oeis4.)