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A090056 Numbers k divisible by at least one nontrivial permutation (rearrangement) of the digits of k, excluding all permutations that result in digit loss. 4

%I

%S 3105,7128,7425,8316,8712,9513,9801,30105,31050,37125,42741,44172,

%T 67128,70416,71208,71253,71280,71328,71928,72108,72441,74142,74250,

%U 74628,74925,78912,79128,80712,81816,82755,83160,83181,83916,84510

%N Numbers k divisible by at least one nontrivial permutation (rearrangement) of the digits of k, excluding all permutations that result in digit loss.

%C Trivial permutations are identified as those where the permutation = k itself. Digit loss occurs when a permutation has 0 in the most significant position, which drops off, leaving a number with fewer digits. For example, when k is 3105, the permutation 0315 is excluded because 315 has fewer digits than 3105. These exclusions make this sequence a subsequence of A090055. A084687 is a subsequence of this sequence.

%C Apparently each term of this sequence is divisible by 3. This has been confirmed for the first 100 terms.

%H Harvey P. Dale, <a href="/A090056/b090056.txt">Table of n, a(n) for n = 1..362</a>

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

%e a(1)=3105 because 3105 is divisible by 1035, a nontrivial permutation of 3105 with the same number of digits.

%e a(4)=8316 because 8316 is divisible by 1386, a nontrivial permutation of 8316 with the same number of digits.

%t dnpQ[n_]:=Module[{d=FromDigits/@Select[Permutations[IntegerDigits[n]], First[#]>0&&Reverse[#]!=#&]},Count[Divisible[n,d],True]>1]; Select[ Range[90000],dnpQ] (* _Harvey P. Dale_, Aug 19 2013 *)

%Y Cf. A084687, A090055, A090061.

%K base,nonn

%O 1,1

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

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Last modified October 1 11:02 EDT 2022. Contains 357147 sequences. (Running on oeis4.)