%I #4 Sep 15 2021 16:48:33
%S 1750842,15922035,17508420,19750842
%N Numbers n which divide the number formed when their digits are sorted in descending order excluding trivial cases.
%C Trivial cases are identified as those values of n where the digits are already in descending order, like 3210 or 8222, such that DSort(n)=n. In such cases DSort(n)/n is equivalent to n/n (as in 3210/3210).
%C a(1) and a(2) are primitive. Clearly if DSort(n) mod n = 0, then dsort(n x 10) mod (n x 10) = 0. Therefore since 1750842 is a member, so will be 17508420, 175084200, 1750842000 and so on. The nonprimitive member 19750842 sets up the implication that 1(9...)750842 is a member. A quick test of 199750842, 1999750842 and 19999750842 seems to confirm this.
%H C. Seggelin, <a href="http://www.plastereddragon.com/maths/asortdiv.htm">Numbers Divisible by Digit Permutations</a>.
%e a(1)=1750842 because the digits of 1750842 in descending order are 8754210 which is divisible by 1750842. a(24)=3105 because the digits of 3105 in ascending order are 135 and 3105 is divisible by 135.
%t sdoQ[n_] := Module[{rs = FromDigits[ReverseSort[ IntegerDigits[n]]]},
%t rs != n && Divisible[rs, n]]; Select[Range[198*10^5],sdoQ] (* _Harvey P. Dale_, Sep 15 2021 *)
%Y Cf. A084687, A090053.
%K base,nonn
%O 1,1
%A Chuck Seggelin (barkeep(AT)plastereddragon.com), Nov 21 2003
