A088032 Smallest number k such that k^n -1 is divisible by an n-th power. a(n) = A088031(n)^(1/n).

3, 3, 9, 3, 33, 31, 129, 31, 513, 511, 2049, 1023, 8193, 8191, 32769, 4095, 131073, 131071, 524289, 262143, 2097153, 2097151, 8388609, 2097151

Offset

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..24.

Example

a(4) = 81 = 3^4 and 81-1 = 80 == 0 (mod 2^4).

Crossrefs

Cf. A088031.

Sequence in context: A337461 A157031 A113213 * A348397 A066572 A307379

Adjacent sequences: A088029 A088030 A088031 * A088033 A088034 A088035

Keyword

more,nonn

Author

Amarnath Murthy, Sep 19 2003

Extensions

Corrected and extended by Ray Chandler, Oct 04 2003

More terms from David Wasserman, Jun 21 2005

More terms from Ryan Propper, Jul 21 2006

a(21)-a(24) from Lars Blomberg, Feb 09 2016

Status

approved