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%I #19 Aug 28 2014 11:23:10
%S 3,8,27,64,125,216,343,512,729,1000,1331,1728,2197,2744,3375,4096,
%T 4913,5832,6859,8000,9261,10648,12167,13824,15625,17576,19683,21952,
%U 24389,27000,29791,32768,35937,39304,42875,46656,50653,54872,59319,64000
%N (a(n)^7+1)/(n^7+1) is the smallest integer > 1.
%H Harry J. Smith, <a href="/A066023/b066023.txt">Table of n, a(n) for n=1..200</a>
%F Conjecture: a(n) = A000578(n), n>1. - _R. J. Mathar_, Aug 28 2014
%F Empirical g.f.: x*(2*x^4-8*x^3+13*x^2-4*x+3) / (x-1)^4. - _Colin Barker_, Aug 28 2014
%t Do[k = 1; While[m = (k^7 + 1)/(n^7 + 1); m < 2 || !IntegerQ[m], k++ ]; Print[k], {n, 1, 40} ]
%o (PARI) { for (n=1, 200, f=n^7 + 1; a=n + 1; while (frac((a^7 + 1)/f) !=0, a++); write("b066023.txt", n, " ", a) ) } \\ _Harry J. Smith_, Nov 07 2009
%Y Cf. A065964.
%K easy,nonn
%O 1,1
%A _Robert G. Wilson v_, Dec 11 2001
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