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Numbers n such that n | 9^n + 8^n + 7^n + 6^n + 5^n + 4^n + 3^n.
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%I #5 Apr 03 2019 11:19:39

%S 1,2,3,4,7,9,10,14,21,27,28,49,50,63,70,81,98,147,153,189,196,243,250,

%T 343,350,441,490,567,686,729,1029,1071,1250,1323,1372,1701,1750,2156,

%U 2187,2188,2401,2450,3087,3430,3969,4802,5103,6250,6561,7203,7497,7546

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

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

%t Select[Range[8000],Divisible[Total[Range[3,9]^#],#]&] (* _Harvey P. Dale_, Apr 03 2019 *)

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Sep 22 2000