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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 Robert Israel, Table of n, a(n) for n = 1..10000 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 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

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