A125135 Triangle read by rows in which row n lists prime factors of p^p - 1 where p = prime(n).

3, 2, 13, 2, 2, 11, 71, 2, 3, 29, 4733, 2, 5, 15797, 1806113, 2, 2, 3, 53, 264031, 1803647, 2, 2, 2, 2, 10949, 1749233, 2699538733, 2, 3, 3, 109912203092239643840221, 2, 11, 461, 1289, 831603031789, 1920647391913

Offset: 1

Author

N. J. A. Sloane, Jan 21 2007

Keywords

• nonn
• tabf

Examples

			Triangle begins:
3;
2, 13;
2, 2, 11, 71;
2, 3, 29, 4733;
2, 5, 15797, 1806113;
2, 2, 3, 53, 264031, 1803647;
2, 2, 2, 2, 10949, 1749233, 2699538733;
2, 3, 3, 109912203092239643840221;
2, 11, 461, 1289, 831603031789, 1920647391913;
2, 2, 7, 59, 16763, 84449, 2428577, 14111459, 58320973, 549334763;
...
n=4: p=7, 7^7-1 = 823542 = 2*3*29*4733 gives row 4.
		

Links

• Sam Wagstaff, Factorizations of p^p - 1 for most p < 180

Crossrefs

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

Programs

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

Maple

T:= n-> (p-> sort(map(i-> i[1]$i[2], ifactors(p^p-1)[2]))[])(ithprime(n)):
seq(T(n), n=1..10);  # Alois P. Heinz, May 20 2022