A060444 Table T(n,k) in which n-th row lists prime factors of 2^n + 1 (n >= 0), without repetition.

2, 3, 5, 3, 17, 3, 11, 5, 13, 3, 43, 257, 3, 19, 5, 41, 3, 683, 17, 241, 3, 2731, 5, 29, 113, 3, 11, 331, 65537, 3, 43691, 5, 13, 37, 109, 3, 174763, 17, 61681, 3, 43, 5419, 5, 397, 2113, 3, 2796203, 97, 257, 673, 3, 11, 251, 4051

Offset

0,1

Comments

Rows have irregular lengths.

The length of row n is A046799(n).

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.)

J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

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

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

Example

Triangle begins:
  2;
  3;
  5;
  3,17;
  3,11;
  5,13;
  3,43;
  257;
  ...

Mathematica

Flatten[Table[Transpose[FactorInteger[2^n+1]][[1]], {n, 0, 25}]] (* Harvey P. Dale, Aug 10 2011 *)

Prog

(PARI) apply( A060444_row(n)=factor(2^n+1)[, 1]~, [0..10]) \\ M. F. Hasler, Nov 19 2018

Crossrefs

Cf. A001269 (factors with repetition), A046799 (number of prime divisors).

Sequence in context: A209195 A113222 A366671 * A002587 A152814 A280319

Adjacent sequences: A060441 A060442 A060443 * A060445 A060446 A060447

Keyword

nonn,tabf

Author

N. J. A. Sloane

Status

approved