The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A338327 a(n) is the least number k such that there are exactly n biquadratefree powerful numbers (A338325) between k^2 and (k+1)^2. 6
 1, 2, 14, 36, 234, 3510, 211297, 487425, 20136429 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is the least k such that A338326(k) = n. Dehkordi (1998) proved that for each k>=0 the sequence of numbers m such that A338326(m) = k has a positive asymptotic density. Therefore, this sequence is infinite. a(9) > 10^10. - Bert Dobbelaere, Oct 29 2020 LINKS Massoud H. Dehkordi, Asymptotic formulae for some arithmetic functions in number theory, Ph.D. thesis, Loughborough University, 1998. EXAMPLE a(0) = 1 since there are no biquadratefree powerful numbers between 1^2 = 1 and 2^2 = 4. a(1) = 2 since there is one biquadratefree powerful number, 8 = 2^3, between 2^2 = 4 and 3^2 = 8. a(2) = 14 since there are 2 biquadratefree powerful numbers, 200 = 2^3 * 5^2 and 216 = 2^3 * 3^3, between 14^2 = 196 and 15^2 = 225. MATHEMATICA bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3 }, #] &]; f[n_] := Count[Range[n^2 + 1, (n + 1)^2 - 1], _?bqfpowQ]; mx = 5; s = Table[0, {mx}]; c = 0; n = 1; While[c < mx, i = f[n] + 1; If[i <= mx && s[[i]] == 0, c++; s[[i]] = n]; n++]; s CROSSREFS Cf. A119242, A337737, A338325, A338326. Sequence in context: A330672 A135706 A091520 * A322226 A218546 A254964 Adjacent sequences:  A338324 A338325 A338326 * A338328 A338329 A338330 KEYWORD nonn,more AUTHOR Amiram Eldar, Oct 22 2020 EXTENSIONS a(8) from Bert Dobbelaere, Oct 29 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 27 18:27 EDT 2021. Contains 346308 sequences. (Running on oeis4.)