A338388 Numbers k such that there is a single biquadratefree powerful number (A338325) between k^2 and (k+1)^2.

2, 5, 8, 10, 11, 18, 19, 22, 25, 33, 37, 42, 46, 48, 51, 52, 53, 55, 57, 58, 59, 65, 70, 73, 78, 87, 88, 92, 94, 96, 102, 103, 104, 109, 111, 114, 115, 116, 119, 121, 122, 135, 144, 145, 149, 150, 155, 157, 164, 165, 166, 176, 181, 182, 183, 185, 190, 191, 195

Offset

1,1

Comments

Positions of 1's in A338326.

The asymptotic density of this sequence is 0.308276695... (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

2 is a term since there is a single biquadratefree powerful number, 8 = 2^3, between 2^2 = 4 and (2+1)^2 = 9.

Mathematica

bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[200], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?bqfpowQ] == 1 &]

Crossrefs

Cf. A336176, A338325, A338326, A338327, A338387, A338389, A338390, A338391, A338392.

Sequence in context: A080228 A153052 A352142 * A237525 A290578 A294127

Adjacent sequences: A338385 A338386 A338387 * A338389 A338390 A338391

Keyword

nonn

Author

Amiram Eldar, Oct 23 2020

Status

approved