A090053 - OEIS

%I #4 May 08 2021 23:37:04

%S 105,108,405,510,540,702,703,810,1001,1005,1008,1020,1050,1080,2002,

%T 2016,2025,2040,2050,2100,3003,3042,3060,3105,3510,4004,4005,4050,

%U 4080,4200,5005,5010,5040,5049,5100,5130,5200,5400,6006,6084

%N Numbers divisible by the number formed when their digits are sorted in ascending order, excluding trivial cases.

%C Trivial cases are identified as (1) values of k where the digits are already in ascending order, like 123 or 2228, such that ASort(k)=k, or (2) values of k where k mod 10 = 0 and all digits other than trailing zeros are in ascending order, like 12000 or 333500, such that ASort(k)=k/10^z, where z = the number of trailing zeros of k. In case (1), k/ASort(k) is equivalent to k/k (as in 123/123). In case (2), k/ASort(k) is 10^z (as in 12000/12). Neither of these cases is very interesting.

%C Sequence A084687 is a subsequence of this sequence, but that sequence excludes any value of k with 1 or more zero digits.

%H C. Seggelin, <a href="http://www.plastereddragon.com/maths/asortdiv.htm">Numbers Divisible by Digit Permutations</a>.

%e a(1)=105 because the digits of 105 in ascending order are 015 and 105 is divisible by 15. a(24)=3105 because the digits of 3105 in ascending order are 135 and 3105 is divisible by 135.

%Y Cf. A084687, A090055, A090056.

%K base,nonn

%O 1,1

%A Chuck Seggelin (barkeep(AT)plastereddragon.com), Nov 21 2003