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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 29 03:50 EDT 2021. Contains 346340 sequences. (Running on oeis4.)