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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
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 &]
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 23 2020
STATUS
approved