Search: id:A109675
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%I A109675
%S A109675 1,4,5,10,25,50,100,446,1000,9775,10000,100000
%N A109675 Numbers n such that the sum of the digits of (n^n - 1) is divisible by 
               n.
%C A109675 n = 10^k is a member of the sequence, for all k >= 0. Proof: Let n = 
               10^k for some nonnegative integer k. Then n^n - 1 has k*10^k 9's 
               and no other digits, so its digits sum to 9*k*10^k = 9*k*n, a multiple 
               of n.
%e A109675 The digits of 9775^9775 - 1 sum to 175950 and 175950 is divisible by 
               9775, so 9775 is in the sequence.
%t A109675 Do[k = n^n - 1; s = Plus @@ IntegerDigits[k]; If[Mod[s, n] == 0, Print[n]], 
               {n, 1, 10^5}]
%Y A109675 Sequence in context: A054173 A049898 A166577 this_sequence A052508 A074098 
               A126069
%Y A109675 Adjacent sequences: A109672 A109673 A109674 this_sequence A109676 A109677 
               A109678
%K A109675 base,hard,more,nonn
%O A109675 1,2
%A A109675 Ryan Propper (rpropper(AT)stanford.edu), Aug 06 2005

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