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Number of numbers b>1 such that n is a repunit in base b representation.
5

%I #7 Jan 22 2014 16:39:53

%S 0,1,1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,3,1,1,1,1,

%T 1,1,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,1,

%U 1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1

%N Number of numbers b>1 such that n is a repunit in base b representation.

%C is a(n) < 4 ?;

%C n>2: a(n) > 0 as n = (n-1)^1 + (n-1)^0.

%C a(A119598(n)) > 3; a(A053696(n)) > 2; a(A085104(n)) > 2. - _Reinhard Zumkeller_, Jan 22 2014

%H Reinhard Zumkeller, <a href="/A088323/b088323.txt">Table of n, a(n) for n = 2..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>

%e a(31)=3: 31 = 2^4+2^3+2^2+2^1+2^0 = 5^2+5^1+5^0 = 30^1+30^0.

%o (Haskell)

%o a088323 n = sum $ map (f n) [2 .. n-1] where

%o f x b = if x == 0 then 1 else if d /= 1 then 0 else f x' b

%o where (x',d) = divMod x b

%o -- _Reinhard Zumkeller_, Jan 22 2014

%Y Cf. A000225, A003462, A002275, A068953.

%K nonn,base

%O 2,6

%A _Reinhard Zumkeller_, Nov 06 2003

%E Example corrected by _Reinhard Zumkeller_, Jan 22 2014