A216471 - OEIS

%I #20 Aug 27 2020 05:41:43

%S 1,3,271,61535,50812751,21358519,237419801716063,1135029771535910655,

%T 8972959412935210028959,91620671606331844031,

%U 1599468651197092802422012477487,702649782312030280795815963215,978557919186290794806960014681034796687

%N Smallest k such that k*n^4 + 1 is an n-th power.

%e a(3) = 271 because 271*3^4 + 1 = 21952 = 28^3.

%t a={}; Do[k = 2; While[ !IntegerQ[(k^n - 1)/n^4], k++ ]; AppendTo[a, (k^n-1)/n^4], {n, 1, 20}]; a

%Y Cf. A076943, A193746, A216439.

%K nonn

%O 1,2

%A _Michel Lagneau_, Sep 10 2012