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

Author

N. J. A. Sloane

Keywords

• nonn
• tabf

Comments

Rows have irregular lengths.

The length of row n is A046799(n).

Examples

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

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.

Crossrefs

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

Programs

Mathematica

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

PARI

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