A088040 - OEIS

%I #14 Dec 05 2013 19:56:32

%S 16,81,81,81,2401,50625,923521,15752961,260144641,4228250625,

%T 68184176641,1095222947841,17557851463681,281200199450625,

%U 4501401006735361,72040003462430721,1152780773560811521

%N Smallest fourth power k such that k-1 is divisible by an n-th power, k > 1.

%C a(2)=a(3)=a(4) as every odd fourth power is == 1 mod (2^4).

%F Empirical g.f.: x*(81920*x^7 -75776*x^6 -45184*x^5 +43696*x^4 -2840*x^3 -2530*x^2 +415*x -16) / ((x-1)*(2*x-1)*(4*x-1)*(8*x-1)*(16*x-1)). [_Colin Barker_, Feb 05 2013]

%e a(5) = 2401 = 7^4 and 7^4 -1 = (2^5)*3*5^2.

%e a(6) = 50625 = 15^4 and 15^4 -1 = (2^6)*7*113.

%Y Cf. A088041.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Sep 19 2003

%E Corrected and extended by _Ray Chandler_, Oct 04 2003