This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A220365 #16 Aug 06 2017 22:39:06
%S A220365 1,70,486,35,10,90,805,5218,243,1,35,1494,469004,1045,288,116,7,195,
%T A220365 29,70,16710,23,2,1017,28,58,162,166,209,486,205,106,1206,2053,37120
%N A220365 a(n) is conjectured to be the largest power k for which k divides the sum of digits of n^k.
%C A220365 a(36) >= 423378.
%C A220365 Please consult the argument in A067863 for the reason that it is believed that all individual such sequences (all k's which divide b^k) terminate.
%F A220365 If a(n) = k, then a(10*n) = k.
%e A220365 a(2) = 70 since the sum of digits of 2^70 is divisible by 70 and it is believed that there does not exist any larger exponent which satisfies this criterion.
%t A220365 For any individual base, b, fQ[n_] := Mod[Plus @@ IntegerDigits[b^n], n] == 0; k = 1; lst = {}; While[k < 100001, If[ fQ@ k, AppendTo[lst, k]; Print[k]]; k++]; lst
%Y A220365 Numbers n such that n divides the sum of digits of k^n: A175169 (k=2), A067862 (k=3), A067864 (k=6), A067863 (k=7), A062933 (k=8), A062927 (k=9), A175525 (k=13), A175589 (k=21), A220364 (k=36), A175552 (k=167).
%K A220365 base,nonn
%O A220365 1,2
%A A220365 _Robert G. Wilson v_, Dec 12 2012
%E A220365 Definition and example corrected by _Giovanni Resta_, Dec 14 2012