login
Table T(n,k) in which n-th row lists prime factors of 2^n + 1 (n >= 0), without repetition.
4

%I #27 Jun 29 2022 10:26:55

%S 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,

%T 3,11,331,65537,3,43691,5,13,37,109,3,174763,17,61681,3,43,5419,5,397,

%U 2113,3,2796203,97,257,673,3,11,251,4051

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

%C Rows have irregular lengths.

%C The length of row n is A046799(n).

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

%H T. D. Noe, <a href="/A060444/b060444.txt">Rows n = 0..500 of triangle, flattened</a> (derived from Brillhart et al.)

%H J. Brillhart et al., <a href="http://dx.doi.org/10.1090/conm/022">Factorizations of b^n +- 1</a>, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

%H S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>.

%H Chai Wah Wu, <a href="https://github.com/postvakje/Reformatted-Cunningham-Project-tables">Tables from the Cunningham Project in machine-readable JSON format.</a>

%e Triangle begins:

%e 2;

%e 3;

%e 5;

%e 3,17;

%e 3,11;

%e 5,13;

%e 3,43;

%e 257;

%e ...

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

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

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

%K nonn,tabf

%O 0,1

%A _N. J. A. Sloane_