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

2, 4, 3, 9, 16, 22, 18, 7, 11, 30, 5, 25, 67, 191, 10, 26, 100, 121, 211, 581, 676, 6, 36, 49, 79, 87, 165, 6205, 178, 13, 47, 501, 562, 29, 37, 68, 135, 163, 565, 900, 1369, 1712, 3446, 4624, 8, 64, 74, 81, 137, 373, 439, 1451, 1816, 2629, 7527, 39209

Offset: 1

Author

T. D. Noe, Apr 03 2013

Keywords

• nonn
• tabf

Comments

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.

Examples

			Irregular triangle:
2:  {},
3:  {},
5:  {},
7:  {2, 4},
11: {},
13: {3, 9, 16, 22},
17: {18},
19: {7, 11},
23: {},
29: {30},
31: {5, 25, 67, 191},
37: {10, 26, 100, 121, 211, 581, 676},
41: {},
43: {6, 36, 49, 79, 87, 165},
47: {6205},
53: {},
59: {178},
61: {13, 47, 501, 562},
67: {29, 37, 68, 135, 163, 565, 900, 1369, 1712, 3446, 4624},
71: {},
73: {8, 64, 74, 81, 137, 373, 439, 1451, 1816, 2629, 7527, 39209}
		

Crossrefs

Cf. A175607 (largest number k such that the greatest prime factor of k^2-1 is prime(n)).

Cf. A223701-A223707 (related sequences).

Programs

Mathematica

t = Table[FactorInteger[n^3 - 1][[-1,1]], {n, 2, 10^6}]; Table[1 + Flatten[Position[t, Prime[n]]], {n, 25}]