A330813 - OEIS

%I #9 Nov 16 2021 07:20:12

%S 1,2,4,6,8,12,18,24,36,48,60,72,96,120,144,168,180,240,336,360,480,

%T 600,630,672,720,840,1080,1260,1440,1680,2160,2520,3360,4320,5040,

%U 7560,10080,15120,20160,25200,27720,30240,40320,45360,50400,55440,60480,75600,83160

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

%C Indices of records of A080221.

%H Amiram Eldar, <a href="/A330813/b330813.txt">Table of n, a(n) for n = 1..64</a>

%e 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.

%t 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

%Y Cf. A005349, A049445, A080221.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Jan 01 2020