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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Initially (up to two-digit numbers) members match with those of A071249. The following are members of this sequence. (1) Numbers made of even digits (GCD >= 2). (2) Numbers with sum of digits a multiple of 3 (GCD >= 3). (3) Numbers using only one digit (k*repunit, k = 1 to 9, GCD = the number itself). It is conjectured that there are no other members.

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. A071249, A084433.

Sequence in context: A154771 A071249 A084433 * A034709 A178158 A034838

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

STATUS

approved

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Last modified October 17 15:27 EDT 2019. Contains 328116 sequences. (Running on oeis4.)