

A144972


Power6free 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
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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

Robert Israel, Table of n, a(n) for n = 1..10000
Richard C. Orr, On the Schnirelmann density of the sequence of kfree integers, Journal of the London Mathematical Society, Vol. 1, No. 1 (1969), pp. 313319.


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

Subsequences: A005117, A004709, A046100, A067259, A051903.
Cf. A013664
Sequence in context: A130696 A146297 A296876 * A166719 A272159 A227981
Adjacent sequences: A144969 A144970 A144971 * A144973 A144974 A144975


KEYWORD

nonn


AUTHOR

Vladimir Joseph Stephan Orlovsky, Sep 27 2008


STATUS

approved



