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

3, 5, 19, 49, 17, 26, 295, 107, 649, 153, 323, 69, 145, 719, 3151, 3841, 251, 597, 6499, 362, 8821, 10165, 3527, 1399, 2981, 836, 1063, 21169, 7289, 3254, 607, 9899, 4045, 21304, 13067, 3431, 867, 803, 57799, 9183, 1601, 27527, 6159, 26459, 10993, 20538

Offset: 1

Author

Benoit Cloitre, Dec 08 2001

Keywords

• nonn

Comments

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, ...).

Links

• Harry J. Smith, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A065876.

Programs

Mathematica

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

PARI

a(n) = { my(r=n^3+1, k=n+1); while ((k^3 + 1)%r, k++); k } \\ Harry J. Smith, Nov 04 2009

Extensions

Corrected and extended by Robert G. Wilson v, Dec 11 2001