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A001265 Table T(n,k) in which n-th row lists prime factors of 2^n - 1 (n >= 2), with repetition. 6
0, 1, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

T. D. Noe, Rows n = 0..500 of triangle, flattened (derived from Brillhart et al.)

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

EXAMPLE

Table begins:

  0;

  1;

  3;

  7;

  3, 5;

  31;

  3, 3, 7;

  127;

  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: A193534 A096247 A122583 * A060443 A020810 A248895

Adjacent sequences:  A001262 A001263 A001264 * A001266 A001267 A001268

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 18 02:20 EST 2018. Contains 299297 sequences. (Running on oeis4.)