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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
OFFSET
1,1
COMMENTS
Positions of 3's in A338326.
The asymptotic density of this sequence is 0.008234579... (Dehkordi, 1998).
LINKS
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 &]
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 23 2020
STATUS
approved