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

Author

Amiram Eldar, Oct 23 2020

Keywords

• nonn

Comments

Positions of 1's in A338326.

The asymptotic density of this sequence is 0.308276695... (Dehkordi, 1998).

Examples

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

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

Programs

Mathematica

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