A007571 a(n) = largest prime factor of n^n + 1.

2, 5, 7, 257, 521, 97, 911, 673, 530713, 27961, 58367, 2227777, 79301, 176597, 142111, 67280421310721, 45957792327018709121, 33388093, 870542161121, 4406613081041681, 22864311556633, 73194743542229, 1522029233, 27250359649

Offset: 1

Author

N. J. A. Sloane, Robert G. Wilson v

Keywords

• nonn
• hard

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Tyler Busby, Table of n, a(n) for n = 1..148 (terms 1..123 from Hugo Pfoertner, terms 124..135 from Yurii Ivanov)
• factordb, Status of 148^148+1 ... 167^167+1.

Crossrefs

Cf. A006530, A006486, A014566, A056790.

Programs

Magma

[Max(PrimeDivisors(n^n+1)):n in [1..24]]; // Marius A. Burtea, Aug 24 2019

Mathematica

Table[ FactorInteger[ n^n + 1, FactorComplete -> True ] [ [ -1, 1 ] ], {n, 1, 25} ]

PARI

for(k=1, 24, my(x=factor(k^k+1), f=x[#x[, 1], 1]); print1(f,", ")) \\ Hugo Pfoertner, Aug 23 2019

Formula

a(n) = A006530(A014566(n)). - Michel Marcus, Aug 24 2019