A057263 Numbers n such that n | 12^n + 11^n + 10^n + 9^n + 8^n + 7^n + 6^n.

1, 3, 7, 9, 21, 27, 49, 63, 81, 93, 99, 147, 189, 243, 343, 387, 441, 539, 567, 729, 777, 1029, 1323, 1701, 1953, 1971, 2079, 2183, 2187, 2401, 3087, 3969, 5103, 6561, 7077, 7203, 7533, 8019, 9261, 9423, 11277, 11319, 11907, 15309, 16807, 17739, 19683

Offset: 1

Author

Robert G. Wilson v, Sep 22 2000

Keywords

• nonn

Programs

Mathematica

Select[ Range[ 10^5 ], Mod[ PowerMod[ 12, #, # ] + PowerMod[ 11, #, # ] + PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ] + PowerMod[ 7, #, # ] + PowerMod[ 6, #, # ], # ] == 0 & ]
With[{c=Range[6,12]},Select[Range[20000],Divisible[Total[c^#],#]&]] (* Harvey P. Dale, Feb 29 2012 *)