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%I #5 Oct 23 2020 18:18:51
%S 3510,3611,16871,25076,26910,35810,50501,83107,101287,104686,111836,
%T 152924,153433,217983,239163,247301,262413,266282,277635,294453,
%U 298950,340228,344510,362830,369877,385336,475063,524827,536793,537713,539293,567062,568609,614283
%N Numbers k such that there are exactly five biquadratefree powerful numbers (A338325) between k^2 and (k+1)^2.
%C Positions of 5's in A338326.
%C The asymptotic density of this sequence is 0.000011113... (Dehkordi, 1998).
%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 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.
%t bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[25000], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?bqfpowQ] == 5 &]
%Y Cf. A338325, A338326, A338327, A338387, A338388, A338389, A338390, A338391.
%K nonn
%O 1,1
%A _Amiram Eldar_, Oct 23 2020