A125136 Triangle read by rows in which row n gives list of prime factors of p^p + 1 where p = prime(n).

5, 2, 2, 7, 2, 3, 521, 2, 2, 2, 113, 911, 2, 2, 3, 23, 89, 199, 58367, 2, 7, 13417, 20333, 79301, 2, 3, 3, 45957792327018709121, 2, 2, 5, 108301, 1049219, 870542161121, 2, 2, 2, 3, 47, 139, 1013, 1641281, 52626071, 1522029233, 2, 3, 5, 233, 6864997

Offset: 1

Author

N. J. A. Sloane, Jan 21 2007

Keywords

• nonn
• tabf

Comments

Product over the n-th row of the table is A051674(n) + 1. The number of elements in the n-th row is A115973(n). - R. J. Mathar, Jan 22 2007

(p + 1) divides p^p + 1 for odd prime p. - Alexander Adamchuk, Jan 22 2007

Examples

			Rows read
  5;
  2, 2, 7;
  2, 3, 521;
  2, 2, 2, 113, 911;
  2, 2, 3, 23, 89, 199, 58367;
  2, 7, 13417, 20333, 79301;
  2, 3, 3, 45957792327018709121;
  2, 2, 5, 108301, 1049219, 870542161121;
  2, 2, 2, 3, 47, 139, 1013, 1641281, 52626071, 1522029233;
  2, 3, 5, 233, 6864997, 9487923853, 5639663878716545087233;
  2, 2, 2, 2, 2, 373, 1613, 62869, 145577, 35789156484227, 2706690202468649;
  etc.
		

Links

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

Crossrefs

Cf. A088730, A125135.

Cf. A007571 = largest factor of n^n + 1.

Programs

Maple

pfs := proc(n) local ifs,a,e,b ; ifs := ifactors(n)[2] ; a := [] ; for b from 1 to nops(ifs) do for e from 1 to op(2,op(b,ifs)) do a := [op(a),op(1,op(b,ifs))] ; od ; od ; RETURN(a) ; end; A125136 := proc(nmax) local a,p,n,pp ; a := [] ; p := 2 ; while nops(a) < nmax do a := [op(a),op(pfs(p^p+1))] ; p := nextprime(p) ; od ; RETURN(a) ; end; A125136(40) ; # R. J. Mathar, Jan 22 2007

Mathematica

lpf[n_]:=Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]; lpf/@(#^#+1&/@ Prime[Range[10]])//Flatten (* Harvey P. Dale, Oct 18 2020 *)

Extensions

More terms from Alexander Adamchuk and R. J. Mathar, Jan 22 2007