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Triangle read by rows in which row n lists prime factors of p^p - 1 where p = prime(n).
11

%I #20 Sep 08 2022 08:45:28

%S 3,2,13,2,2,11,71,2,3,29,4733,2,5,15797,1806113,2,2,3,53,264031,

%T 1803647,2,2,2,2,10949,1749233,2699538733,2,3,3,

%U 109912203092239643840221,2,11,461,1289,831603031789,1920647391913

%N Triangle read by rows in which row n lists prime factors of p^p - 1 where p = prime(n).

%H Sam Wagstaff, <a href="http://homes.cerias.purdue.edu/~ssw/bell/r1">Factorizations of p^p - 1 for most p < 180</a>

%e Triangle begins:

%e 3;

%e 2, 13;

%e 2, 2, 11, 71;

%e 2, 3, 29, 4733;

%e 2, 5, 15797, 1806113;

%e 2, 2, 3, 53, 264031, 1803647;

%e 2, 2, 2, 2, 10949, 1749233, 2699538733;

%e 2, 3, 3, 109912203092239643840221;

%e 2, 11, 461, 1289, 831603031789, 1920647391913;

%e 2, 2, 7, 59, 16763, 84449, 2428577, 14111459, 58320973, 549334763;

%e ...

%e n=4: p=7, 7^7-1 = 823542 = 2*3*29*4733 gives row 4.

%p T:= n-> (p-> sort(map(i-> i[1]$i[2], ifactors(p^p-1)[2]))[])(ithprime(n)):

%p seq(T(n), n=1..10); # _Alois P. Heinz_, May 20 2022

%o (Magma) for p in [ n : n in [1..100] | IsPrime(n) ] do "\nDoing p =", p; n := p^p -1; Factorisation(n); end for; // _John Cannon_

%Y Cf. A006486, A088730, A125136, A212552, A214812.

%K nonn,tabf

%O 1,1

%A _N. J. A. Sloane_, Jan 21 2007