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A338391 Numbers k such that there are exactly four biquadratefree powerful numbers (A338325) between k^2 and (k+1)^2. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Positions of 4's in A338326.
The asymptotic density of this sequence is 0.000089634... (Dehkordi, 1998).
LINKS
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
Sequence in context: A256086 A186897 A184450 * A304615 A287878 A252338
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 23 2020
STATUS
approved

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Last modified February 23 14:24 EST 2024. Contains 370283 sequences. (Running on oeis4.)