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%I #12 Aug 28 2016 04:09:11
%S 2,5,11,14,15,18,22,31,36,41,45,46,52,55,58,70,76,82,88,89,90,96,103,
%T 110,117,129,132,140,148,156,164,172,181,189,198,207,225,234,243,252,
%U 262,272,279,281,291,301,311,316,322,332,353,362,364,374,385,396,401
%N Numbers n such that the interval n^2 < x < (n+1)^2 contains at least one nonsquare perfect power A097054.
%H T. D. Noe, <a href="/A097055/b097055.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) ~ n^(3/2). - _Charles R Greathouse IV_, Aug 28 2016
%e 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.
%t 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 *)
%o (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
%Y Cf. A000290, A097054, A097056.
%K nonn
%O 1,1
%A _Hugo Pfoertner_, Jul 21 2004
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