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 A097056 Numbers n such that the interval n^2 < x < (n+1)^2 contains two or more distinct nonsquare perfect powers A097054. 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Empirically, there seem to be no intervals between consecutive squares containing more than two nonsquare perfect powers. LINKS T. D. Noe, Table of n, a(n) for n = 1..180 (using the b-file 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: 2536^2n^2 && !ispower(t) && s++ > 1, return(1))); 0 \\ Charles R Greathouse IV, Dec 11 2012 (PARI) haspow(lower, upper, eMin, eMax)=if(sqrtnint(upper, 3)^3>lower, return(1)); forprime(e=eMin, eMax, if(sqrtnint(upper, e)^e>lower, return(1))); 0 list(lim)=lim\=1; my(v=List(), M=(lim+1)^2, L=logint(M, 2), s); forprime(e=5, L, forprime(p=2, sqrtnint(M, e), s=sqrtint(p^e); if(haspow(s^2, (s+1)^2-1, e+1, L) && s<=lim, listput(v, s)))); Set(v) \\ Charles R Greathouse IV, Nov 05 2015 CROSSREFS Cf. A000290, A097054, A097055. Sequence in context: A222368 A276300 A222476 * A092358 A079029 A106953 Adjacent sequences:  A097053 A097054 A097055 * A097057 A097058 A097059 KEYWORD nonn AUTHOR Hugo Pfoertner, Jul 21 2004 EXTENSIONS a(5)-a(20) from Don Reble a(21)-a(26) from David Wasserman, Dec 17 2007 STATUS approved

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Last modified March 20 13:57 EDT 2018. Contains 300985 sequences. (Running on oeis4.)