A066023 (a(n)^7+1)/(n^7+1) is the smallest integer > 1.

3, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653, 54872, 59319, 64000

Offset: 1

Author

Robert G. Wilson v, Dec 11 2001

Keywords

• easy
• nonn

Links

• Harry J. Smith, Table of n, a(n) for n=1..200

Crossrefs

Cf. A065964.

Programs

Mathematica

Do[k = 1; While[m = (k^7 + 1)/(n^7 + 1); m < 2 || !IntegerQ[m], k++ ]; Print[k], {n, 1, 40} ]

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

Formula

Conjecture: a(n) = A000578(n), n>1. - R. J. Mathar, Aug 28 2014

Empirical g.f.: x*(2*x^4-8*x^3+13*x^2-4*x+3) / (x-1)^4. - Colin Barker, Aug 28 2014