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A330812
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Least number >= n that is a Niven number in all bases 1 <= b <= n.
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0
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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
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OFFSET
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1,2
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LINKS
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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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]
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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