A193745 - OEIS

%I #5 Mar 30 2012 18:35:58

%S 1,4,57,26,216145205,1232644,16412938630073477961847,1678453230184,

%T 5043695769339201738285763848771292,

%U 38634088549546746345278764872265967473783

%N Smallest k  such that k*n! +1 is an n-th power.

%e a(3) = 57 because 57*3!+1 = 343 = 7^3.

%t a={};Do[k = 2;While[ !IntegerQ[(k^n - 1)/n!], k++ ]; AppendTo[a,(k^n-1)/n!],{n, 1, 10}];a

%K nonn

%O 1,2

%A _Michel Lagneau_, Aug 03 2011