OFFSET
1,1
COMMENTS
Positions of 5's in A338326.
The asymptotic density of this sequence is 0.000011113... (Dehkordi, 1998).
LINKS
Massoud H. Dehkordi, Asymptotic formulae for some arithmetic functions in number theory, Ph.D. thesis, Loughborough University, 1998.
EXAMPLE
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.
MATHEMATICA
bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[25000], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?bqfpowQ] == 5 &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 23 2020
STATUS
approved