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A338389
Numbers k such that there are exactly two biquadratefree powerful numbers (A338325) between k^2 and (k+1)^2.
6
14, 31, 67, 72, 82, 93, 98, 110, 132, 140, 156, 172, 189, 192, 223, 240, 257, 281, 285, 322, 347, 368, 379, 407, 410, 414, 426, 441, 455, 468, 472, 481, 488, 514, 515, 517, 524, 525, 537, 551, 555, 574, 579, 602, 613, 664, 680, 693, 702, 703, 737, 743, 749, 755
OFFSET
1,1
COMMENTS
Positions of 2's in A338326.
The asymptotic density of this sequence is 0.058757863... (Dehkordi, 1998).
LINKS
Massoud H. Dehkordi, Asymptotic formulae for some arithmetic functions in number theory, Ph.D. thesis, Loughborough University, 1998.
EXAMPLE
14 is a term since there are exactly two biquadratefree powerful numbers, 200 = 2*3 * 5^2 and 216 = 2^3 * 3^3, between 14^2 = 196 and (14+1)^2 = 225.
MATHEMATICA
bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[800], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?bqfpowQ] == 2 &]
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 23 2020
STATUS
approved