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%I #7 Jan 19 2015 12:25:57
%S 1,7,11,49,77,121,343,539,847,1331,2401,3773,5929,9317,11473,14641,
%T 16807,26411,34111,41503,44737,57233,59339,65219,102487,117649,161051,
%U 184877,197351,290521,309827,456533,717409,823543,919583,953239
%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.
%C The naive heuristic suggests that this sequence is infinite. - _Charles R Greathouse IV_, Dec 10 2013
%t Select[ Range[ 10^6 ], Mod[ PowerMod[ 12, #, # ] + PowerMod[ 11, #, # ] + PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ] + PowerMod[ 7, #, # ] + PowerMod[ 6, #, # ] + PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 3, #, # ] + PowerMod[ 2, #, # ], # ] == 0 & ]
%t Select[Range[10^6],Mod[Total[Table[PowerMod[i,#,#],{i,2,12}]],#]==0&] (* This program is substantially identical to the first Mathematica program above *) (* _Harvey P. Dale_, Jan 19 2015 *)
%o (PARI) is(n)=sum(k=2,12,Mod(k,n)^n)==0 \\ _Charles R Greathouse IV_, Dec 10 2013
%K nonn
%O 1,2
%A _Robert G. Wilson v_, Sep 22 2000
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