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 A090054 Numbers n which divide the number formed when their digits are sorted in descending order excluding trivial cases. 0
 1750842, 15922035, 17508420, 19750842 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 21 01:14 EDT 2024. Contains 374462 sequences. (Running on oeis4.)