

A097056


Numbers n such that the interval n^2 < x < (n+1)^2 contains two or more distinct nonsquare perfect powers A097054.


6



5, 11, 46, 2536, 558640, 572783, 3362407, 7928108, 8928803, 67460050, 106938971, 1763350849, 2501641555, 2756149047, 4584349318, 5713606932, 17941228664, 375376083513, 411124334926, 452894760105, 1167680330892, 1933159894790, 1946131548918, 2506032014606, 2507269866902, 8217688694093
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OFFSET

1,1


COMMENTS

Empirically, there seem to be no intervals between consecutive squares containing more than two nonsquare perfect powers. a(5)..a(20) from Don Reble (djr(AT)nk.ca).


LINKS

T. D. Noe, Table of n, a(n) for n = 1..180 (using the bfile from A117934)


EXAMPLE

a(1)=5: 5^2<3^3<2^5<6^2, a(2)=11: 11^2<5^3<2^7<12^2, a(4)=2536: 2536^2<x<2537^2 (6431296,6436369) contains 23^5=6436343 and 186^3=6434856.
22 is not in the sequence because 2^9 and 8^3 (22^2<512<23^2) are not distinct.


PROG

(PARI) is(n)=my(s, t); forprime(p=3, 2*log(n+1.5)\log(2), t=floor((n+1)^(2/p)); if(t^p>n^2 && !ispower(t) && s++ > 1, return(1))); 0 \\ Charles R Greathouse IV, Dec 11 2012


CROSSREFS

Cf. A000290, A097054, A097055.
Sequence in context: A141355 A222368 A222476 * A092358 A079029 A106953
Adjacent sequences: A097053 A097054 A097055 * A097057 A097058 A097059


KEYWORD

nonn


AUTHOR

Hugo Pfoertner, Jul 21 2004


EXTENSIONS

More terms from David Wasserman, Dec 17 2007


STATUS

approved



