The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #9 Oct 24 2020 04:03:22
%S 234,675,2426,8075,8391,9093,9548,10214,10340,11213,13816,14523,14970,
%T 15593,17329,17803,20649,22483,23020,23128,24842,25971,26318,26557,
%U 28241,28677,29124,29837,31058,31338,31732,31907,32490,35676,35765,36302,37599,41077,42577
%N Numbers k such that there are exactly four biquadratefree powerful numbers (A338325) between k^2 and (k+1)^2.
%C Positions of 4's in A338326.
%C The asymptotic density of this sequence is 0.000089634... (Dehkordi, 1998).
%H Amiram Eldar, <a href="/A338391/b338391.txt">Table of n, a(n) for n = 1..600</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 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.
%t bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[10^4], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?bqfpowQ] == 4 &]
%Y Cf. A338325, A338326, A338327, A338387, A338388, A338389, A338390, A338392.
%K nonn
%O 1,1
%A _Amiram Eldar_, Oct 23 2020