A001265 Table T(n,k) in which n-th row lists prime factors of 2^n - 1 (n >= 2), with repetition.
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
Offset: 2
Examples
Table begins: n=2: 3; n=3: 7; n=4: 3, 5; n=5: 31; n=6: 3, 3, 7; n=7: 127; n=8: 3, 5, 17; ...
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
- Max Alekseyev, Rows n = 2..1206, flattened (rows 2..500 from T. D. Noe)
- 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
- Chai Wah Wu, Tables from the Cunningham Project in machine-readable JSON format.
Programs
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Mathematica
Array[Flatten[ConstantArray[#1, #2] & @@ # & /@ FactorInteger[2^# - 1]] &, 24] // Flatten (* Michael De Vlieger, Dec 04 2017 *)
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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
Extensions
Ambiguous rows 0 and 1 removed by Max Alekseyev, Jul 25 2023
Comments