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A144972 Power-6-free numbers: numbers whose exponents in their prime factorization are all less than 6. 1
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Superset of A005117 and A067259. The first numbers not in the sequence are 64, 128, 192, 256, 320, 384, 448, 512, 576, 640, 704, 729 etc. [R. J. Mathar, Oct 11 2008]
This sequence has an asymptotic density of about 0.98270. - David A. Corneth, Nov 05 2017
From Amiram Eldar, Mar 20 2021: (Start)
The asymptotic density of this sequence is 1/zeta(6) = 1/A013664 = 945/Pi^6 = 0.9829525922...
The Schnirelmann density of this sequence is 6165/6272 (Orr, 1969). (End)
LINKS
Richard C. Orr, On the Schnirelmann density of the sequence of k-free integers, Journal of the London Mathematical Society, Vol. 1, No. 1 (1969), pp. 313-319.
FORMULA
{n: A051903(n) <= 5}. [R. J. Mathar, Oct 11 2008, corrected Oct 19 2008]
MAPLE
select(n -> max(seq(f[2], f=ifactors(n)[2]))<=5, [$1..1000]); # Robert Israel, Nov 05 2017
MATHEMATICA
lst={}; Do[a=0; Do[If[FactorInteger[m][[n, 2]]>5, a=1], {n, Length[FactorInteger[m]]}]; If[a!=1, AppendTo[lst, m]], {m, 2*5!}]; lst
Select[Range[100], AllTrue[FactorInteger[#][[;; , 2]] , #1 < 6 & ] &] (* Amiram Eldar, Mar 20 2021 *)
CROSSREFS
Sequence in context: A130696 A146297 A296876 * A166719 A272159 A227981
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)