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A338388
Numbers k such that there is a single biquadratefree powerful number (A338325) between k^2 and (k+1)^2.
6
2, 5, 8, 10, 11, 18, 19, 22, 25, 33, 37, 42, 46, 48, 51, 52, 53, 55, 57, 58, 59, 65, 70, 73, 78, 87, 88, 92, 94, 96, 102, 103, 104, 109, 111, 114, 115, 116, 119, 121, 122, 135, 144, 145, 149, 150, 155, 157, 164, 165, 166, 176, 181, 182, 183, 185, 190, 191, 195
OFFSET
1,1
COMMENTS
Positions of 1's in A338326.
The asymptotic density of this sequence is 0.308276695... (Dehkordi, 1998).
LINKS
Massoud H. Dehkordi, Asymptotic formulae for some arithmetic functions in number theory, Ph.D. thesis, Loughborough University, 1998.
EXAMPLE
2 is a term since there is a single biquadratefree powerful number, 8 = 2^3, between 2^2 = 4 and (2+1)^2 = 9.
MATHEMATICA
bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[200], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?bqfpowQ] == 1 &]
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 23 2020
STATUS
approved