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

0,3

Comments

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

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.

Example

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)

Mathematica

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

Crossrefs

Cf. A001265, A064078.

Sequence in context: A362026 A122583 A001265 * A020810 A248895 A021732

Adjacent sequences: A060440 A060441 A060442 * A060444 A060445 A060446

Keyword

nonn,tabf

Author

N. J. A. Sloane

Status

approved