

A001265


Table T(n,k) in which nth 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
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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, Machinereadable 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^n1), 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



