

A338390


Numbers k such that there are exactly three biquadratefree powerful numbers (A338325) between k^2 and (k+1)^2.


6



36, 161, 364, 659, 722, 771, 896, 911, 981, 987, 1241, 1359, 1486, 1575, 1822, 2042, 2090, 2435, 2537, 2582, 2733, 2870, 2873, 2967, 2983, 3012, 3101, 3108, 3198, 3222, 3278, 3419, 3465, 3544, 3668, 3855, 3860, 3934, 4024, 4092, 4188, 4426, 4437, 4494, 4511, 4522
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OFFSET

1,1


COMMENTS

Positions of 3's in A338326.
The asymptotic density of this sequence is 0.008234579... (Dehkordi, 1998).


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..6500
Massoud H. Dehkordi, Asymptotic formulae for some arithmetic functions in number theory, Ph.D. thesis, Loughborough University, 1998.


EXAMPLE

36 is a term since there are exactly three biquadratefree powerful numbers, 1323 = 3^3 * 7^2, 1331 = 11^3 and 1352 = 2^3 * 13^2, between 36^2 = 1296 and (36+1)^2 = 1369.


MATHEMATICA

bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[1000], Count[Range[#^2 + 1, (# + 1)^2  1], _?bqfpowQ] == 3 &]


CROSSREFS

Cf. A336178, A338325, A338326, A338327, A338387, A338388, A338389, A338391, A338392.
Sequence in context: A280397 A064500 A264474 * A268905 A017054 A231972
Adjacent sequences: A338387 A338388 A338389 * A338391 A338392 A338393


KEYWORD

nonn


AUTHOR

Amiram Eldar, Oct 23 2020


STATUS

approved



