login
Numbers n such that n | 10^n + 9^n + 8^n + 7^n + 6^n + 5^n + 4^n + 3^n + 2^n.
0

%I #5 Aug 14 2013 16:01:17

%S 1,2,3,4,6,9,12,21,27,63,81,147,189,243,441,567,678,729,996,1029,1323,

%T 1449,1572,1701,2187,2781,3087,3969,5103,6561,7203,8444,8754,9261,

%U 11907,13041,13293,15309,19683,21609,23667,23949,25188,26019,27491

%N Numbers n such that n | 10^n + 9^n + 8^n + 7^n + 6^n + 5^n + 4^n + 3^n + 2^n.

%t Select[ Range[ 10^5 ], Mod[ PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ] + PowerMod[ 7, #, # ] + PowerMod[ 6, #, # ] + PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 3, #, # ] + PowerMod[ 2, #, # ], # ] == 0 & ]

%t Select[Range[30000],Divisible[Total[Range[2,10]^#],#]&] (* _Harvey P. Dale_, Aug 14 2013 *)

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Sep 22 2000