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%I #4 Jun 03 2013 14:59:11
%S 7,8,8,8,8,12,12,24,24,24,24,24,24,432,720,720,720,720,720,840,840,
%T 840,3360,13860,13860,13860,13860,13860,40320,100800,100800,2106720,
%U 7698600,9028800,9028800,9028800,9028800,9028800,9028800,9028800,9028800,9028800
%N a(n) is the smallest k > 6 such that k is a Niven number at least in all the bases from 1 to n.
%C The bound a(i) > 6 is motivated by the fact that 1, 2, 4 and 6 are Niven numbers in every base.
%H Giovanni Resta, <a href="/A226320/b226320.txt">Table of n, a(n) for n = 1..54</a>
%e a(8) = 24 because 24 is the smallest k > 6 which is Niven in bases 1 (trivial), 2,..., 8. For example, 24 = (33)_7 = (44)_5 = (220)_3.
%t a[n_] := Block[{k=7}, n > 1 && While[ Max@ Mod[k, Total /@ IntegerDigits[k, Range[2, n]]] > 0, k++]; k]; Array[a, 20]
%Y Cf. A005349, A226169, A226319, A225427 (Niven in bases 1,...,n but not in base n+1).
%K nonn,base
%O 1,1
%A _Giovanni Resta_, Jun 03 2013
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