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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

Harvey P. Dale, Table of n, a(n) for n = 1..362

C. Seggelin, Numbers Divisible by Digit Permutations.

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

Cf. A084687, A090055, A090061.

Sequence in context: A103523 A345519 A234265 * A229410 A257356 A187593

Adjacent sequences:  A090053 A090054 A090055 * A090057 A090058 A090059

KEYWORD

base,nonn

AUTHOR

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

STATUS

approved

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Last modified August 10 11:03 EDT 2022. Contains 356039 sequences. (Running on oeis4.)