A088323 Number of numbers b>1 such that n is a repunit in base b representation.

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, 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, 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

Offset: 2

Author

Reinhard Zumkeller, Nov 06 2003

Keywords

• nonn
• base

Comments

is a(n) < 4 ?;

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

a(A119598(n)) > 3; a(A053696(n)) > 2; a(A085104(n)) > 2. - Reinhard Zumkeller, Jan 22 2014

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 2..10000
• Eric Weisstein's World of Mathematics, Repunit

Crossrefs

Cf. A000225, A003462, A002275, A068953.

Programs

Haskell

a088323 n = sum $ map (f n) [2 .. n-1] where
   f x b = if x == 0 then 1 else if d /= 1 then 0 else f x' b
                                 where (x',d) = divMod x b
-- Reinhard Zumkeller, Jan 22 2014

Extensions

Example corrected by Reinhard Zumkeller, Jan 22 2014