A338389 Numbers k such that there are exactly two biquadratefree powerful numbers (A338325) between k^2 and (k+1)^2.

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

Author

Amiram Eldar, Oct 23 2020

Keywords

• nonn

Comments

Positions of 2's in A338326.

The asymptotic density of this sequence is 0.058757863... (Dehkordi, 1998).

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Massoud H. Dehkordi, Asymptotic formulae for some arithmetic functions in number theory, Ph.D. thesis, Loughborough University, 1998.

Crossrefs

Cf. A336177, A338325, A338326, A338327, A338387, A338388, A338390, A338391, A338392.

Programs

Mathematica

bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[800], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?bqfpowQ] == 2 &]