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A001269 Table T(n,k) in which n-th row lists prime factors of 2^n + 1 (n >= 0), with repetition.

%I A001269 #36 Feb 29 2024 23:08:14
%S A001269 2,3,5,3,3,17,3,11,5,13,3,43,257,3,3,3,19,5,5,41,3,683,17,241,3,2731,
%T A001269 5,29,113,3,3,11,331,65537,3,43691,5,13,37,109,3,174763,17,61681,3,3,
%U A001269 43,5419,5,397,2113,3,2796203,97,257,673,3,11,251,4051
%N A001269 Table T(n,k) in which n-th row lists prime factors of 2^n + 1 (n >= 0), with repetition.
%C A001269 Rows have irregular lengths.
%C A001269 The length of row n is A054992(n).
%D A001269 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 A001269 Max Alekseyev, <a href="/A001269/b001269.txt">Rows n = 0..1122, flattened</a> (rows 0..500 from T. D. Noe)
%H A001269 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 A001269 Ricardo Gómez Aíza, <a href="https://arxiv.org/abs/2402.16111">Trees with flowers: A catalog of integer partition and integer composition trees with their asymptotic analysis</a>, arXiv:2402.16111 [math.CO], 2024. See p. 23.
%H A001269 S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>
%H A001269 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 A001269 Triangle begins:
%e A001269   2;
%e A001269   3;
%e A001269   5;
%e A001269   3,3,17;
%e A001269   3,11;
%e A001269   5,13;
%e A001269   3,43;
%e A001269   257;
%e A001269   ...
%t A001269 repeat[{p_, e_}] := Table[p, {e}]; row[n_] := repeat /@ FactorInteger[2^n + 1] // Flatten; Table[row[n], {n, 0, 25}] // Flatten (* _Jean-François Alcover_, Jul 13 2012 *)
%o A001269 (PARI) apply( A001269_row(n)=concat(apply(f->vector(f[2],i,f[1]), Col(factor(2^n+1))~)), [0..19]) \\ _M. F. Hasler_, Nov 19 2018
%Y A001269 Cf. A060444 (factors w/o repetition), A054992 (row lengths).
%K A001269 nonn,tabf
%O A001269 0,1
%A A001269 _N. J. A. Sloane_