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 A097055 Numbers n such that the interval n^2 < x < (n+1)^2 contains at least one nonsquare perfect power A097054. 4
 2, 5, 11, 14, 15, 18, 22, 31, 36, 41, 45, 46, 52, 55, 58, 70, 76, 82, 88, 89, 90, 96, 103, 110, 117, 129, 132, 140, 148, 156, 164, 172, 181, 189, 198, 207, 225, 234, 243, 252, 262, 272, 279, 281, 291, 301, 311, 316, 322, 332, 353, 362, 364, 374, 385, 396, 401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 FORMULA a(n) ~ n^(3/2). - Charles R Greathouse IV, Aug 28 2016 EXAMPLE a(1)=2 because 2^2<2^3<3^2, a(2)=5: 5^2<3^3<2^5<6^2, a(3)=11: 11^2<5^3<2^7<12^2. MATHEMATICA nn=1000^2; pp=Select[Union[Flatten[Table[n^i, {i, Prime[Range[2, PrimePi[Log[2, nn]]]]}, {n, 2, nn^(1/i)}]]], !IntegerQ[Sqrt[#]]&]; Union[Floor[Sqrt[pp]]] (* T. D. Noe, Apr 19 2011 *) PROG (PARI) is(n)=my(n2=n^2, t=n2+2*n); for(e=3, logint(t, 2), if(sqrtnint(t, e)^e>n2, return(1))); 0 \\ Charles R Greathouse IV, Aug 28 2016 CROSSREFS Cf. A000290, A097054, A097056. Sequence in context: A224793 A272852 A210506 * A251536 A347838 A191163 Adjacent sequences: A097052 A097053 A097054 * A097056 A097057 A097058 KEYWORD nonn AUTHOR Hugo Pfoertner, Jul 21 2004 STATUS approved

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Last modified September 22 10:36 EDT 2023. Contains 365520 sequences. (Running on oeis4.)