A330813 Numbers k that are Niven numbers in a record number of bases 1 <= b <= k.

1, 2, 4, 6, 8, 12, 18, 24, 36, 48, 60, 72, 96, 120, 144, 168, 180, 240, 336, 360, 480, 600, 630, 672, 720, 840, 1080, 1260, 1440, 1680, 2160, 2520, 3360, 4320, 5040, 7560, 10080, 15120, 20160, 25200, 27720, 30240, 40320, 45360, 50400, 55440, 60480, 75600, 83160

Offset: 1

Author

Amiram Eldar, Jan 01 2020

Keywords

• nonn
• base

Comments

Indices of records of A080221.

Examples

			4 is a term since it is a Niven number in 4 bases: 1, 2, 3, 4, while the numbers below 4 are Niven numbers in less than 4 bases.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..64

Crossrefs

Cf. A005349, A049445, A080221.

Programs

Mathematica

nivenQ[n_, b_] := Divisible[n, Total @ IntegerDigits[n, b]]; basesCount[n_] := 1 + Sum[Boole @ nivenQ[n, b], {b, 2, n}]; bmax = 0; seq = {}; Do[b = basesCount[n]; If[b > bmax ,bmax = b; AppendTo[seq,n]],{n,1,1000}];seq