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%I #5 Aug 05 2017 11:24:56
%S 1,2,3,9,10,13,26,27,39,50,81,110,117,130,169,243,250,279,310,338,351,
%T 470,507,550,650,663,729,1053,1209,1250,1430,1521,1550,1690,2187,2197,
%U 2750,3159,3250,3410,4030,4043,4069,4394,4509,4563,6250,6561,6591,7150
%N 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^n.
%t Select[ Range[ 10^5 ], Mod[ PowerMod[ 12, #, # ] + PowerMod[ 11, #, # ] + PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ] + PowerMod[ 7, #, # ] + PowerMod[ 6, #, # ] + PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 3, #, # ] + PowerMod[ 2, #, # ] + 1, # ] == 0 & ]
%t Select[Range[7200],Divisible[Total[Range[12]^#],#]&] (* _Harvey P. Dale_, Aug 05 2017 *)
%K nonn
%O 1,2
%A _Robert G. Wilson v_, Sep 22 2000
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