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a(n) is the smallest k such that (k^4 + 1)/(n^4 + 1) is an integer > 1.
1

%I #8 Jun 16 2018 19:00:20

%S 3,8,27,64,125,216,343,474,43,781,1331,1728,2197,1807,3375,4096,4913,

%T 1600,807,8000,9261,10648,12167,13824,7353,17576,6721,21952,24389,

%U 27000,29791,32768,35937,39304,42875,46656,50653,4015,59319,20723

%N a(n) is the smallest k such that (k^4 + 1)/(n^4 + 1) is an integer > 1.

%H Harry J. Smith, <a href="/A066018/b066018.txt">Table of n, a(n) for n = 1..250</a>

%t Do[k = 1; While[m = (k^4 + 1)/(n^4 + 1); m < 2 || !IntegerQ[m], k++ ]; Print[k], {n, 1, 40} ]

%o (PARI) { for (n=1, 250, f=n^4 + 1; a=n + 1; while (frac((a^4 + 1)/f) !=0, a++); write("b066018.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