A330812 Least number >= n that is a Niven number in all bases 1 <= b <= n.

1, 2, 4, 4, 6, 6, 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, 9028800

Offset: 1

Author

Amiram Eldar, Jan 01 2020

Keywords

• nonn
• base

Examples

			a(4) = 4 since the representations of 4 in bases 1 to 4 are 1111, 100, 11, 10, the corresponding sums of digits are 4, 1, 2, and 1, and all are divisors of 4. Thus 4 is a Niven number in bases 1, 2, 3, and 4, and it is the least number with this property.
		

Crossrefs

Cf. A005349, A049445, A080221, A226169.

Programs

Maple

A[1]:= 1: m:= 1:
for n from 2 while m < 30 do
   kk:= n;
   for k from 2 to n-1 do
     if n mod convert(convert(n,base,k),`+`) <> 0 then kk:= k-1; break fi;
     od;
   if kk > m then
     for k from m+1 to kk do A[k]:= n od;
     m:= kk;
   fi
od:
seq(A[k],k=1..m); # Robert Israel, Jan 01 2020

Mathematica

nivenQ[n_, b_] := Divisible[n, Total @ IntegerDigits[n,b]]; a[n_] := Module[{k = n}, While[!AllTrue[Range[2, n], nivenQ[k, #] &], k++]; k]; Array[a,30]