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Numbers n such that n | 7^n + 6^n + 5^n + 4^n + 3^n + 2^n + 1^n.
1

%I #7 Mar 12 2018 17:43:22

%S 1,2,4,7,10,14,28,49,50,70,98,196,209,250,343,350,490,539,668,686,

%T 1250,1309,1372,1519,1750,1919,2401,2450,2690,2849,3430,4450,4802,

%U 6250,8750,9212,9590,9604,9982,10717,12250,15698,16807,17150,18790,24010,31250

%N Numbers n such that n | 7^n + 6^n + 5^n + 4^n + 3^n + 2^n + 1^n.

%t Do[ If[ Mod[ PowerMod[ 7, n, n ] + PowerMod[ 6, n, n ] + PowerMod[ 5, n, n ] + PowerMod[ 4, n, n ] + PowerMod[ 3, n, n ] + PowerMod[ 2, n, n ] + 1, n ] == 0, Print[ n ] ], {n, 1, 10^6} ]

%t Select[Range[31500],Divisible[Plus@@(Range[7]^#),#]&] (* or *) Select[ Range[ 31500],Mod[Total[PowerMod[Range[7],#,#]],#]==0&] (* The second program is much faster than the first, and the second program is only a rewrite of the first program above *) (* _Harvey P. Dale_, Mar 12 2018 *)

%Y Cf. A001554.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Aug 25 2000