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%I #12 Feb 09 2016 14:26:00
%S 3,3,9,3,33,31,129,31,513,511,2049,1023,8193,8191,32769,4095,131073,
%T 131071,524289,262143,2097153,2097151,8388609,2097151
%N Smallest number k such that k^n -1 is divisible by an n-th power. a(n) = A088031(n)^(1/n).
%C For 2 < n < 18, if n is odd then a(n) = 2^n+1 and if n is even then a(n) = 2^(n-A007814(n))-1. - _David Wasserman_, Jun 21 2005
%C The above also holds for 19 < n < 24. If true for n >= 25 then a(25..29) = 33554433, 33554431, 134217729, 67108863, 536870913. - _Lars Blomberg_, Feb 09 2016
%e a(4) = 81 = 3^4 and 81-1 = 80 == 0 (mod 2^4).
%Y Cf. A088031.
%K more,nonn
%O 1,1
%A _Amarnath Murthy_, Sep 19 2003
%E Corrected and extended by _Ray Chandler_, Oct 04 2003
%E More terms from _David Wasserman_, Jun 21 2005
%E More terms from _Ryan Propper_, Jul 21 2006
%E a(21)-a(24) from _Lars Blomberg_, Feb 09 2016