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Numbers k such that k | 12^k + 11^k + 10^k + 9^k + 8^k + 7^k + 6^k + 5^k.
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%I #17 Nov 30 2022 11:20:39

%S 1,2,4,10,17,50,62,221,250,253,289,290,316,697,764,1250,1819,3590,

%T 4913,6250,31250,54043,55913,63869,83521,98923,156250,231250,530893,

%U 781250,987110,1419857,2383750,3906250,4531250,6891250,8789357,9593750,12479450,18458141,19531250

%N Numbers k such that k | 12^k + 11^k + 10^k + 9^k + 8^k + 7^k + 6^k + 5^k.

%t Select[Range[1000000],Divisible[Total[PowerMod[Range[5,12],#,#]],#]&] (* _Harvey P. Dale_, Mar 28 2012 *)

%o (Python)

%o [n for n in range(1,20000000) if sum(pow(k,n,n) for k in range(5,13)) % n == 0] # _Lucas A. Brown_, Nov 30 2022

%Y Cf. A057490.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Sep 22 2000

%E a(32)-a(42) from _Lucas A. Brown_, Nov 30 2022