This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A089584 #12 Jun 08 2025 16:15:42
%S A089584 10,21,40,100,112,120,210,306,400,516,624,630,1000,1010,1102,1320,
%T A089584 1344,1422,2223,2240,2301,3430,4000,10000,10100,10101,10356,10360,
%U A089584 11220,12320,13440,14220,20202,21112,21210,21416,22400,30303,33036,34300
%N A089584 Numbers n which are a proper multiple (>1) of A068505(n) (= n read in base m+1 where m = largest digit of n).
%C A089584 Terms > 9 in A089583 without digit "9". - _M. F. Hasler_, Apr 05 2009
%C A089584 This sequence excludes the trivial terms of A089583. Note that all single-digit numbers are excluded as they equal themselves when converted to base b+1. 3 in base 4 is 3 and of course divides the original value of 3. Note also that all numbers containing the digit 9 can only be interpreted as base-10 numbers, which of course divide themselves once and are therefore excluded. See sequence A089583 for the full sequence including trivial terms.
%e A089584 a(5)=112 because 112 in base 3 yields 14 in base 10, which evenly divides 112 (112/14 = 8). a(21)=2301 because 2301 in base 4 yields 177, which evenly divides 2301 (2301/177=13).
%o A089584 (PARI) is_A089584(n,d,b)={ 10>(b=1+vecmax(d=eval(Vec(Str(n))))) & n%sum(i=1,#d,d[i]*b^(#d-i))==0 }
%Y A089584 Cf. A054055 (largest digit of n), A068505 (n as base b+1 number where b=largest digit of n), A089583 (n mod A068505(n) = 0).
%K A089584 base,nonn
%O A089584 1,1
%A A089584 _Chuck Seggelin_, Nov 08 2003
%E A089584 Definition reworded by _M. F. Hasler_, Apr 05 2009