A066020 - OEIS

%I #8 Jun 16 2018 19:00:39

%S 3,8,27,64,125,118,343,512,729,1000,1331,1728,2197,2744,3375,4096,

%T 4913,5832,6859,8000,9261,10648,12167,13824,15625,11663,19683,21952,

%U 11189,27000,29791,32768,35937,39304,42875,46656,50653,54872,59319,64000

%N a(n) is the smallest k such that (k^5 + 1)/(n^5 + 1) is an integer > 1.

%H Harry J. Smith, <a href="/A066020/b066020.txt">Table of n, a(n) for n = 1..200</a>

%t Do[k = 1; While[m = (k^5 + 1)/(n^5 + 1); m < 2 || !IntegerQ[m], k++ ]; Print[k], {n, 1, 40} ]

%o (PARI) { for (n=1, 200, f=n^5 + 1; a=n + 1; while (frac((a^5 + 1)/f) !=0, a++); write("b066020.txt", n, " ", a) ) } \\ _Harry J. Smith_, Nov 06 2009

%Y Cf. A065964.

%K easy,nonn

%O 1,1

%A _Robert G. Wilson v_, Dec 11 2001