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A090054 Numbers n which divide the number formed when their digits are sorted in descending order excluding trivial cases. 0

%I

%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

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Last modified August 19 04:40 EDT 2022. Contains 356216 sequences. (Running on oeis4.)