A338387 Numbers k such that there are no biquadratefree powerful numbers (A338325) between k^2 and (k+1)^2.

1, 3, 4, 6, 7, 9, 12, 13, 15, 16, 17, 20, 21, 23, 24, 26, 27, 28, 29, 30, 32, 34, 35, 38, 39, 40, 41, 43, 44, 45, 47, 49, 50, 54, 56, 60, 61, 62, 63, 64, 66, 68, 69, 71, 74, 75, 76, 77, 79, 80, 81, 83, 84, 85, 86, 89, 90, 91, 95, 97, 99, 100, 101, 105, 106, 107

Offset: 1

Author

Amiram Eldar, Oct 23 2020

Keywords

• nonn

Comments

Positions of 0's in A338326.

The asymptotic density of this sequence is 0.623265038... (Dehkordi, 1998).

Examples

			1 is a term since the two numbers between 1^2 = 1 and (1+1)^2 = 4, 2 and 3, are not biquadratefree powerful.
2 is not a term since there is a 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. A336175, A338325, A338326, A338327, A338388, A338389, A338390, A338391, A338392.

Programs

Mathematica

bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[100], !AnyTrue[Range[#^2 + 1, (# + 1)^2 - 1], bqfpowQ] &]