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A097056
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Numbers n such that the interval n^2 < x < (n+1)^2 contains two or more distinct nonsquare perfect powers A097054.
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6
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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
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1,1
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COMMENTS
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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).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..180 (using the b-file from A117934)
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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Cf. A000290, A097054, A097055.
Sequence in context: A141355 A222368 A222476 * A092358 A079029 A106953
Adjacent sequences: A097053 A097054 A097055 * A097057 A097058 A097059
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner, Jul 21 2004
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EXTENSIONS
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More terms from David Wasserman, Dec 17 2007
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STATUS
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approved
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