A084434 Numbers whose digit permutations have GCD > 1.

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

Offset: 1

Author

Amarnath Murthy, Jun 02 2003

Keywords

• base
• nonn
• changed

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

Examples

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

Crossrefs

Cf. A008585, A014181, A014263, A071249.

Subsequence of A084433 which contains for example 592 which is not in here.

Programs

Mathematica

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

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