A001265 Table T(n,k) in which n-th row lists prime factors of 2^n - 1 (n >= 2), with repetition.

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

Offset

2,1

Comments

For n > 1, the length of row n is A046051(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

Max Alekseyev, Rows n = 2..1206, flattened (rows 2..500 from T. D. Noe)

Joerg Arndt, Rows n = 1..1200 of triangle (derived from Brillhart et al.; updated by Jon E. Schoenfield)

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

S. S. Wagstaff, Jr., The Cunningham Project

Eric Weisstein's World of Mathematics, Mersenne Number

Chai Wah Wu, Tables from the Cunningham Project in machine-readable JSON format.

Example

Table begins:
 n=2: 3;
 n=3: 7;
 n=4: 3, 5;
 n=5: 31;
 n=6: 3, 3, 7;
 n=7: 127;
 n=8: 3, 5, 17;
  ...

Mathematica

Array[Flatten[ConstantArray[#1, #2] & @@ # & /@ FactorInteger[2^# - 1]] &, 24] // Flatten (* Michael De Vlieger, Dec 04 2017 *)

Prog

(PARI) row(n)= if (n==1, return ([0])); my(f = factor(2^n-1), v = []); for (i=1, #f~, for (j=1, f[i, 2], v = concat(v, f[i, j]))); v; \\ Michel Marcus, Dec 05 2017

Crossrefs

Cf. A060443, A182590.

Sequence in context: A337013 A362026 A122583 * A060443 A020810 A248895

Adjacent sequences: A001262 A001263 A001264 * A001266 A001267 A001268

Keyword

nonn,tabf

Author

N. J. A. Sloane

Extensions

Ambiguous rows 0 and 1 removed by Max Alekseyev, Jul 25 2023

Status

approved