OFFSET
1,1
COMMENTS
Positions of 4's in A338326.
The asymptotic density of this sequence is 0.000089634... (Dehkordi, 1998).
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.
EXAMPLE
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.
MATHEMATICA
bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[10^4], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?bqfpowQ] == 4 &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 23 2020
STATUS
approved