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A065964 a(n) is the smallest k such that (k^3 + 1)/(n^3 + 1) is an integer > 1. 5

%I

%S 3,5,19,49,17,26,295,107,649,153,323,69,145,719,3151,3841,251,597,

%T 6499,362,8821,10165,3527,1399,2981,836,1063,21169,7289,3254,607,9899,

%U 4045,21304,13067,3431,867,803,57799,9183,1601,27527,6159,26459,10993,20538

%N a(n) is the smallest k such that (k^3 + 1)/(n^3 + 1) is an integer > 1.

%C a(n) exists because n^3 + 1 divides (n^3 - n^2 + 1)^3 + 1. The set S of n such a(n) = n^3 - n^2 + 1 is S = (2, 3, 4, 7, 9, 15, 16, 19, 21, 22, ...).

%H Harry J. Smith, <a href="/A065964/b065964.txt">Table of n, a(n) for n = 1..300</a>

%t Do[k = 1; While[m = (k^3 + 1)/(n^3 + 1); m < 2 || !IntegerQ[m], k++ ]; Print[k], {n, 1, 50} ]

%o (PARI) { for (n=1, 300, a=n + 1; while (frac((a^3 + 1)/(n^3 + 1)), a++); write("b065964.txt", n, " ", a) ) } \\ _Harry J. Smith_, Nov 04 2009

%Y Cf. A065876.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Dec 08 2001

%E Corrected and extended by _Robert G. Wilson v_, Dec 11 2001

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Last modified October 1 08:39 EDT 2020. Contains 337442 sequences. (Running on oeis4.)