A226320 a(n) is the smallest k > 6 such that k is a Niven number at least in all the bases from 1 to n.

7, 8, 8, 8, 8, 12, 12, 24, 24, 24, 24, 24, 24, 432, 720, 720, 720, 720, 720, 840, 840, 840, 3360, 13860, 13860, 13860, 13860, 13860, 40320, 100800, 100800, 2106720, 7698600, 9028800, 9028800, 9028800, 9028800, 9028800, 9028800, 9028800, 9028800, 9028800

Offset: 1

Author

Giovanni Resta, Jun 03 2013

Keywords

• nonn
• base

Comments

The bound a(i) > 6 is motivated by the fact that 1, 2, 4 and 6 are Niven numbers in every base.

Examples

			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.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..54

Crossrefs

Cf. A005349, A226169, A226319, A225427 (Niven in bases 1,...,n but not in base n+1).

Programs

Mathematica

a[n_] := Block[{k=7}, n > 1 && While[ Max@ Mod[k, Total /@ IntegerDigits[k, Range[2, n]]] > 0, k++]; k]; Array[a, 20]