A338391 Numbers k such that there are exactly four biquadratefree powerful numbers (A338325) between k^2 and (k+1)^2.

234, 675, 2426, 8075, 8391, 9093, 9548, 10214, 10340, 11213, 13816, 14523, 14970, 15593, 17329, 17803, 20649, 22483, 23020, 23128, 24842, 25971, 26318, 26557, 28241, 28677, 29124, 29837, 31058, 31338, 31732, 31907, 32490, 35676, 35765, 36302, 37599, 41077, 42577

Offset: 1

Author

Amiram Eldar, Oct 23 2020

Keywords

• nonn

Comments

Positions of 4's in A338326.

The asymptotic density of this sequence is 0.000089634... (Dehkordi, 1998).

Examples

			234 is a term since there are exactly four biquadratefree powerful numbers, 54872 = 2^3 * 19^3, 54925 = 5^2 * 13^3, 55112 = 2^3 * 83^2 and 55125 = 3^2 * 5^3 * 7^2, between 234^2 = 54756 and (234+1)^2 = 55225.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..600
• 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, A338392.

Programs

Mathematica

bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[10^4], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?bqfpowQ] == 4 &]