cp's OEIS Frontend

A223703 Conjectured irregular triangle (with some rows blank) of numbers k such that prime(n) is the largest prime factor of k^3 - 1.

%I A223703 #3 Apr 03 2013 22:50:09
%S A223703 2,4,3,9,16,22,18,7,11,30,5,25,67,191,10,26,100,121,211,581,676,6,36,
%T A223703 49,79,87,165,6205,178,13,47,501,562,29,37,68,135,163,565,900,1369,
%U A223703 1712,3446,4624,8,64,74,81,137,373,439,1451,1816,2629,7527,39209
%N A223703 Conjectured irregular triangle (with some rows blank) of numbers k such that prime(n) is the largest prime factor of k^3 - 1.
%C A223703 Primes 2, 3, 5, 11, 23, 41, 53, 71, 83, 89,... do not appear as largest factors. However, they can be smaller factors. For instance, 3^3 - 1 = 2 * 13.
%e A223703 Irregular triangle:
%e A223703 2:  {},
%e A223703 3:  {},
%e A223703 5:  {},
%e A223703 7:  {2, 4},
%e A223703 11: {},
%e A223703 13: {3, 9, 16, 22},
%e A223703 17: {18},
%e A223703 19: {7, 11},
%e A223703 23: {},
%e A223703 29: {30},
%e A223703 31: {5, 25, 67, 191},
%e A223703 37: {10, 26, 100, 121, 211, 581, 676},
%e A223703 41: {},
%e A223703 43: {6, 36, 49, 79, 87, 165},
%e A223703 47: {6205},
%e A223703 53: {},
%e A223703 59: {178},
%e A223703 61: {13, 47, 501, 562},
%e A223703 67: {29, 37, 68, 135, 163, 565, 900, 1369, 1712, 3446, 4624},
%e A223703 71: {},
%e A223703 73: {8, 64, 74, 81, 137, 373, 439, 1451, 1816, 2629, 7527, 39209}
%t A223703 t = Table[FactorInteger[n^3 - 1][[-1,1]], {n, 2, 10^6}]; Table[1 + Flatten[Position[t, Prime[n]]], {n, 25}]
%Y A223703 Cf. A175607 (largest number k such that the greatest prime factor of k^2-1 is prime(n)).
%Y A223703 Cf. A223701-A223707 (related sequences).
%K A223703 nonn,tabf
%O A223703 1,1
%A A223703 _T. D. Noe_, Apr 03 2013