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

1,2

Comments

Positions of 0's in A338326.

The asymptotic density of this sequence is 0.623265038... (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

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.

Mathematica

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

Crossrefs

Cf. A336175, A338325, A338326, A338327, A338388, A338389, A338390, A338391, A338392.

Sequence in context: A229173 A066499 A201471 * A360799 A136110 A032725

Adjacent sequences: A338384 A338385 A338386 * A338388 A338389 A338390

Keyword

nonn

Author

Amiram Eldar, Oct 23 2020

Status

approved