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Smallest number k such that k^n -1 is divisible by an n-th power. a(n) = A088031(n)^(1/n).
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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