

A338326


The number of biquadratefree powerful numbers (A338325) between the consecutive squares n^2 and (n+1)^2.


8



0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 3, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 1
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OFFSET

1,14


COMMENTS

Dehkordi (1998) proved that for each k>=0 the sequence of numbers m such that a(m) = k has a positive asymptotic density.


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

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


MATHEMATICA

bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3 }, #] &]; a[n_] := Count[Range[n^2 + 1, (n + 1)^2  1], _?bqfpowQ]; Array[a, 100]


CROSSREFS

Cf. A119241, A337736, A338325.
Sequence in context: A296338 A133703 A073265 * A025438 A220400 A285108
Adjacent sequences: A338323 A338324 A338325 * A338327 A338328 A338329


KEYWORD

nonn


AUTHOR

Amiram Eldar, Oct 22 2020


STATUS

approved



