

A084434


Numbers whose digit permutations have GCD > 1.


0



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

1,1


COMMENTS

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


LINKS

Table of n, a(n) for n=1..68.


EXAMPLE

72 is in the sequence because 72 and 27 are both divisible by 9.


MATHEMATICA

Select[Range[0, 150], GCD @@ FromDigits /@ Permutations[IntegerDigits[#]] > 1 &] (* Harvey P. Dale, Jan 12 2011 *)


CROSSREFS

Cf. A008585, A014181, A014263, A071249, A084433.
Sequence in context: A154771 A071249 A084433 * A034709 A178158 A337184
Adjacent sequences: A084431 A084432 A084433 * A084435 A084436 A084437


KEYWORD

base,nonn


AUTHOR

Amarnath Murthy, Jun 02 2003


EXTENSIONS

More terms from David Wasserman, May 07 2004
Initial zero removed, Harvey P. Dale, Jan 14 2011
Entry revised by N. J. A. Sloane, Aug 27 2020


STATUS

approved



