A057286 Numbers k such that k | 11^k + 10^k + 9^k + 8^k + 7^k + 6^k + 5^k + 4^k + 3^k.

1, 3, 7, 9, 21, 27, 49, 63, 69, 81, 119, 147, 189, 243, 343, 441, 567, 729, 1029, 1269, 1323, 1701, 2187, 2401, 3087, 3357, 3969, 5103, 5271, 5831, 6561, 7203, 9261, 9639, 11907, 15309, 16767, 16807, 19683, 20727, 21609, 24451, 27783, 30429, 35077

Offset: 1

Author

Robert G. Wilson v, Sep 22 2000

Keywords

• nonn

Programs

Mathematica

Select[ Range[ 10^5 ], Mod[ PowerMod[ 11, #, # ] + PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ] + PowerMod[ 7, #, # ] + PowerMod[ 6, #, # ] + PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 3, #, # ], # ] == 0 & ]
Select[Range[36000],Mod[Total[Table[PowerMod[n,#,#],{n,3,11}]],#] == 0&] (* This program is essentially equivalent to the above program. *) (* Harvey P. Dale, Jun 09 2021 *)