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A046101 Biquadrateful numbers. 24
16, 32, 48, 64, 80, 81, 96, 112, 128, 144, 160, 162, 176, 192, 208, 224, 240, 243, 256, 272, 288, 304, 320, 324, 336, 352, 368, 384, 400, 405, 416, 432, 448, 464, 480, 486, 496, 512, 528, 544, 560, 567, 576, 592, 608, 624, 625, 640, 648, 656, 672, 688, 704 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The convention in the OEIS is that squareful, cubeful (A046099), biquadrateful, ... mean the same as "not squarefree" etc., while 2- or square-full, 3- or cube-full (A036966), 4-full (A036967) are used for Golomb's notion of powerful numbers (A001694, see references there), when each prime factor occurs to a power > 1. - M. F. Hasler, Feb 12 2008
Also solutions to equation tau_{-3}(n)=0, where tau_{-3} is A007428. - Enrique Pérez Herrero, Jan 19 2013
Sum_{n>0} 1/a(n)^s = Zeta(s) - Zeta(s)/Zeta(4s). - Enrique Pérez Herrero, Jan 21 2013
A051903(a(n)) > 3. - Reinhard Zumkeller, Sep 03 2015
The asymptotic density of this sequence is 1 - 1/zeta(4) = 1 - 90/Pi^4 = 0.076061... - Amiram Eldar, Jul 09 2020
LINKS
Eric Weisstein's World of Mathematics, Biquadratefree.
MAPLE
with(NumberTheory):
isBiquadrateful := n -> is(denom(Radical(n) / LargestNthPower(n, 2)) <> 1):
select(isBiquadrateful, [`$`(1..704)]); # Peter Luschny, Jul 12 2022
MATHEMATICA
lst={}; Do[a=0; Do[If[FactorInteger[m][[n, 2]]>3, a=1], {n, Length[FactorInteger[m]]}]; If[a==1, AppendTo[lst, m]], {m, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 15 2008 *)
Select[Range[1000], Max[Transpose[FactorInteger[#]][[2]]]>3&] (* Harvey P. Dale, May 25 2014 *)
PROG
(Haskell)
a046101 n = a046101_list !! (n-1)
a046101_list = filter ((> 3) . a051903) [1..]
-- Reinhard Zumkeller, Sep 03 2015
(PARI) is(n)=n>9 && vecmax(factor(n)[, 2])>3 \\ Charles R Greathouse IV, Sep 03 2015
CROSSREFS
Sequence in context: A359831 A048111 A122614 * A360723 A044856 A217558
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified May 20 05:07 EDT 2024. Contains 372703 sequences. (Running on oeis4.)