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

1750842, 15922035, 17508420, 19750842

Offset

1,1

Comments

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).

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.

Links

Table of n, a(n) for n=1..4.

C. Seggelin, Numbers Divisible by Digit Permutations.

Example

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.

Mathematica

sdoQ[n_] := Module[{rs = FromDigits[ReverseSort[ IntegerDigits[n]]]},
rs != n && Divisible[rs, n]]; Select[Range[198*10^5], sdoQ] (* Harvey P. Dale, Sep 15 2021 *)

Crossrefs

Cf. A084687, A090053.

Sequence in context: A124068 A244073 A237307 * A186823 A095391 A234456

Adjacent sequences: A090051 A090052 A090053 * A090055 A090056 A090057

Keyword

base,nonn

Author

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

Status

approved