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Irregular triangle read by rows in which row n lists prime factors (with multiplicity) of the repunit (10^n - 1)/9 (A002275(n)).
15

%I #42 Aug 02 2024 11:32:41

%S 1,11,3,37,11,101,41,271,3,7,11,13,37,239,4649,11,73,101,137,3,3,37,

%T 333667,11,41,271,9091,21649,513239,3,7,11,13,37,101,9901,53,79,

%U 265371653,11,239,4649,909091,3,31,37,41,271,2906161,11,17,73,101

%N Irregular triangle read by rows in which row n lists prime factors (with multiplicity) of the repunit (10^n - 1)/9 (A002275(n)).

%C See A003020 for other links and references.

%H <a href="/A102380/b102380.txt">Rows n=1..352, flattened</a>

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/repunit/">Factorizations of 11...11 (repunit)</a>.

%H Yousuke Koide, <a href="https://repunit-koide.jimdofree.com/">Factorizations of Repunit Numbers</a>

%H Franz Lemmermeyer, <a href="https://arxiv.org/abs/1201.0282">Simerka - Quadratic Forms and Factorization</a>, arXiv:1201.0282 [math.NT], 2011. For the 19th row = [2071723, 5363222357].

%H Samuel Yates, <a href="http://www.jstor.org/stable/2689643">The Mystique of Repunits</a>, Math. Mag. 51 (1978), 22-28.

%e First rows:

%e 1;

%e 11;

%e 3, 37;

%e 11, 101;

%e 41, 271;

%e 3, 7, 11, 13, 37;

%e 239, 4649;

%e ...

%p [seq( ifactor((10^n-1)/9),n=1..20)];

%Y Cf. A002275, A067063, A003020, A204845, A204846, A204847, A204848.

%K nonn,tabf

%O 1,2

%A _N. J. A. Sloane_, Nov 28 2006

%E First 100 rows in b-file from _T. D. Noe_, Feb 27 2009

%E Rows n=101..322 in b-file from _Ray Chandler_, May 01 2017

%E Rows n=323..352 in b-file from _Max Alekseyev_, Apr 26 2022