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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
3105, 7128, 7425, 8316, 8712, 9513, 9801, 30105, 31050, 37125, 42741, 44172, 67128, 70416, 71208, 71253, 71280, 71328, 71928, 72108, 72441, 74142, 74250, 74628, 74925, 78912, 79128, 80712, 81816, 82755, 83160, 83181, 83916, 84510 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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.
Apparently each term of this sequence is divisible by 3. This has been confirmed for the first 100 terms.
LINKS
EXAMPLE
a(1)=3105 because 3105 is divisible by 1035, a nontrivial permutation of 3105 with the same number of digits.
a(4)=8316 because 8316 is divisible by 1386, a nontrivial permutation of 8316 with the same number of digits.
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A103523 A345519 A234265 * A229410 A257356 A187593
KEYWORD
base,nonn
AUTHOR
Chuck Seggelin (barkeep(AT)plastereddragon.com), Nov 21 2003
STATUS
approved

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Last modified July 20 19:11 EDT 2024. Contains 374459 sequences. (Running on oeis4.)