A223704 Conjectured irregular triangle (with some rows blank) of numbers k such that prime(n) is the largest prime factor of k^3 + 1.

1, 2, 3, 5, 19, 4, 10, 17, 23, 8, 12, 31, 69, 6, 26, 68, 11, 27, 101, 122, 7, 37, 50, 80, 179, 582, 14, 48, 75, 563, 719, 2820, 4135, 30, 38, 164, 231, 440, 566, 901, 11093, 112925, 267167, 212, 9, 65, 374, 20303, 24, 56, 103, 293, 530, 656, 767, 868, 82, 2157

Offset: 1

Author

T. D. Noe, Apr 03 2013

Keywords

• nonn
• tabf

Comments

Primes 5, 11, 17, 23, 29, 47, 59,... do not appear as largest factors. However, they can be smaller factors. For instance, 4^3 + 1 = 5 * 13.

Examples

			Irregular triangle:
2:  {1},
3:  {2},
5:  {},
7:  {3, 5, 19},
11: {},
13: {4, 10, 17, 23},
17: {},
19: {8, 12, 31, 69},
23: {},
29: {},
31: {6, 26, 68},
37: {11, 27, 101},
41: {122},
43: {7, 37, 50, 80, 179},
47: {},
53: {582},
59: {},
61: {14, 48, 75, 563, 719, 2820, 4135},
67: {30, 38, 164, 231, 440, 566, 901, 11093, 112925, 267167},
71: {212},
73: {9, 65, 374, 20303},
79: {24, 56, 103, 293, 530, 656, 767, 868},
83: {82, 2157}.
		

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, 10^6}]; Table[Flatten[Position[t, Prime[n]]], {n, 25}]