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

1,1

Comments

Positions of 2's in A338326.

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

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.

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 &]

Crossrefs

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

Sequence in context: A344397 A161454 A156203 * A196135 A276301 A101183

Adjacent sequences: A338386 A338387 A338388 * A338390 A338391 A338392

Keyword

nonn

Author

Amiram Eldar, Oct 23 2020

Status

approved