A060443 Table T(n,k) in which n-th row lists prime factors of 2^n - 1 (n >= 2), without repetition.

0, 1, 3, 7, 3, 5, 31, 3, 7, 127, 3, 5, 17, 7, 73, 3, 11, 31, 23, 89, 3, 5, 7, 13, 8191, 3, 43, 127, 7, 31, 151, 3, 5, 17, 257, 131071, 3, 7, 19, 73, 524287, 3, 5, 11, 31, 41, 7, 127, 337, 3, 23, 89, 683, 47, 178481, 3, 5, 7, 13, 17, 241

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• tabf

Comments

For n > 1, the length of row n is A046800(n). - T. D. Noe, Aug 06 2007

Examples

			From _Wolfdieter Lang_, Sep 23 2017: (Start)
The irregular triangle T(n,k) begins for n >= 2:
n\k      1   2    3    4   5
2:       3
3:       7
4:       3   5
5:      31
6:       3   7
7:     127
8:       3   5   17
9:       7  73
10:      3  11   31
11:     23  89
12:      3   5    7   13
13:   8191
14:      3  43  127
15:      7  31  151
16:      3   5   17  257
17: 131071
18:      3   7   19   73
19: 524287
20:      3   5   11   31  41
... (End)
		

References

• J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.

Links

• T. D. Noe, Rows n=0..500 of triangle, flattened (derived from Brillhart et al.)
• Joerg Arndt, Rows n=1..1200 of triangle when repetitions are included (derived from Brillhart et al.)
• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
• Jeroen Demeyer, Machine-readable Cunningham Tables [Broken link]
• S. S. Wagstaff, Jr., The Cunningham Project
• Chai Wah Wu, Tables from the Cunningham Project in machine-readable JSON format.

Crossrefs

Cf. A001265, A064078.

Programs

Mathematica

Array[FactorInteger[2^# - 1][[All, 1]] &, 25, 0] (* Paolo Xausa, Apr 18 2024 *)