A338390 Numbers k such that there are exactly three biquadratefree powerful numbers (A338325) between k^2 and (k+1)^2.

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

Author

Amiram Eldar, Oct 23 2020

Keywords

• nonn

Comments

Positions of 3's in A338326.

The asymptotic density of this sequence is 0.008234579... (Dehkordi, 1998).

Examples

			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.
		

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.

Crossrefs

Cf. A336178, A338325, A338326, A338327, A338387, A338388, A338389, A338391, A338392.

Programs

Mathematica

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