A057290 Numbers n such that n | 12^n + 11^n + 10^n + 9^n + 8^n + 7^n + 6^n + 5^n + 4^n + 3^n + 2^n.

1, 7, 11, 49, 77, 121, 343, 539, 847, 1331, 2401, 3773, 5929, 9317, 11473, 14641, 16807, 26411, 34111, 41503, 44737, 57233, 59339, 65219, 102487, 117649, 161051, 184877, 197351, 290521, 309827, 456533, 717409, 823543, 919583, 953239

Offset

1,2

Comments

The naive heuristic suggests that this sequence is infinite. - Charles R Greathouse IV, Dec 10 2013

Links

Table of n, a(n) for n=1..36.

Mathematica

Select[ Range[ 10^6 ], Mod[ PowerMod[ 12, #, # ] + PowerMod[ 11, #, # ] + PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ] + PowerMod[ 7, #, # ] + PowerMod[ 6, #, # ] + PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 3, #, # ] + PowerMod[ 2, #, # ], # ] == 0 & ]
Select[Range[10^6], Mod[Total[Table[PowerMod[i, #, #], {i, 2, 12}]], #]==0&] (* This program is substantially identical to the first Mathematica program above *) (* Harvey P. Dale, Jan 19 2015 *)

Prog

(PARI) is(n)=sum(k=2, 12, Mod(k, n)^n)==0 \\ Charles R Greathouse IV, Dec 10 2013

Crossrefs

Sequence in context: A117392 A105867 A166653 * A003599 A018508 A038277

Adjacent sequences: A057287 A057288 A057289 * A057291 A057292 A057293

Keyword

nonn

Author

Robert G. Wilson v, Sep 22 2000

Status

approved