A247216 Maximum of the smallest prime factors of (i^prime(n)-1)/(i-1), when i runs through all integers in [2, prime(n)].

3, 13, 31, 55987, 12207031, 16148168401, 50544702849929377, 109912203092239643840221, 11111111111111111111111, 7369130657357778596659, 568972471024107865287021434301977158534824481, 388230138454493

Offset: 1

Author

Vladimir Shevelev, Nov 26 2014

Keywords

• nonn

Comments

If in the definition "maximum" is replaced with "minimum," then we obtain A035095 (see comment there).

Crossrefs

Cf. A020639, A035095.

Programs

Maple

with(numtheory):
a:= n-> max(seq(min(factorset(
        (i^ithprime(n)-1)/(i-1))[]), i=2..ithprime(n))):
seq(a(n), n=1..10);  # Alois P. Heinz, Dec 06 2014

Mathematica

a[n_] := Max[Table[Min[FactorInteger[(i^Prime[n]-1)/(i-1)][[All, 1]]], {i, 2, Prime[n]}]];
Table[a[n], {n, 1, 12}] (* Jean-François Alcover, Mar 25 2017, after Alois P. Heinz *)

Formula

a(n) == 1 (mod prime(n)).

Extensions

More terms from Peter J. C. Moses, Nov 26 2014