A338392 Numbers k such that there are exactly five biquadratefree powerful numbers (A338325) between k^2 and (k+1)^2.

3510, 3611, 16871, 25076, 26910, 35810, 50501, 83107, 101287, 104686, 111836, 152924, 153433, 217983, 239163, 247301, 262413, 266282, 277635, 294453, 298950, 340228, 344510, 362830, 369877, 385336, 475063, 524827, 536793, 537713, 539293, 567062, 568609, 614283

Offset: 1

Author

Amiram Eldar, Oct 23 2020

Keywords

• nonn

Comments

Positions of 5's in A338326.

The asymptotic density of this sequence is 0.000011113... (Dehkordi, 1998).

Examples

			3510 is a term since there are exactly five biquadratefree powerful numbers, 12320648 = 2^3 * 17^2 * 73^2, 12321000 = 2^3 * 3^2 * 5^3 * 37^2, 12324500 = 2^2 * 5^3 * 157^2, 12325975 = 5^2 * 79^3 and 12326391 = 3^3 * 7^3 * 11^3, between 3510^2 = 12320100 and (3510+1)^2 = 12327121.
		

Links

• Massoud H. Dehkordi, Asymptotic formulae for some arithmetic functions in number theory, Ph.D. thesis, Loughborough University, 1998.

Crossrefs

Cf. A338325, A338326, A338327, A338387, A338388, A338389, A338390, A338391.

Programs

Mathematica

bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[25000], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?bqfpowQ] == 5 &]