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A084434
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Numbers whose digit permutations have GCD > 1.
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0
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2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 18, 20, 21, 22, 24, 26, 27, 28, 30, 33, 36, 39, 40, 42, 44, 45, 46, 48, 50, 51, 54, 55, 57, 60, 62, 63, 64, 66, 68, 69, 70, 72, 75, 77, 78, 80, 81, 82, 84, 86, 87, 88, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132
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OFFSET
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1,1
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COMMENTS
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Numbers k such that there is a number d>1 which divides every number that can be obtained by permuting the digits of k. - N. J. A. Sloane, Aug 27 2020
Theorem. The sequence consists of: (1) A008585 (multiples of 3), (2) A014263 (numbers with all digits even), (3) A014181 (numbers with all digits equal), (4) numbers with all digits 5 or 0, (5) numbers with all digits 7 or 0, (6) numbers with 6k digits, all of which are 1 or 8, and (7) numbers with 6k digits, all of which are 2 or 9. - David Wasserman, May 07 2004
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LINKS
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EXAMPLE
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72 is in the sequence because 72 and 27 are both divisible by 9.
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MATHEMATICA
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Select[Range[0, 150], GCD @@ FromDigits /@ Permutations[IntegerDigits[#]] > 1 &] (* Harvey P. Dale, Jan 12 2011 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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Initial zero removed, Harvey P. Dale, Jan 14 2011
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STATUS
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approved
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