A090055 Numbers n divisible by at least one nontrivial permutation (rearrangement) of the digits of n.

105, 108, 405, 510, 540, 702, 703, 810, 1001, 1005, 1008, 1020, 1050, 1053, 1080, 2002, 2016, 2025, 2040, 2050, 2079, 2100, 2106, 3003, 3024, 3042, 3045, 3060, 3105, 3402, 3510, 4004, 4005, 4050, 4070, 4080, 4200, 5005, 5010, 5040

Offset: 1

Author

Chuck Seggelin, Nov 21 2003

Keywords

• base
• nonn

Comments

Trivial permutations are identified as (1) permutation = n, or (2) when n mod 10=0, permutations of n's digits which result in shifting only trailing zeros to the most significant side of n where they drop off, such that permutation = n/10^z, where z <= the number of trailing zeros of n. So if n were 1809000, the following permutations would be excluded as trivial: 1809000, 0180900, 0018090, 0001809.

A031877 (numbers which are multiples of their reversals) and both A084687 and A090053 (numbers divided by number formed by sorting their digits), are subsets of this sequence. This sequence differentiates itself by including terms such as 7425 which is divided by 2475 (a rearrangement of 7425's digits that is neither a reversal or an ascending sort.)

Examples

			a(27)=3045 because 3045 is divisible by 435, a nontrivial permutation of 3045. (0435)
		

Links

• C. Seggelin, Numbers Divisible by Digit Permutations.

Crossrefs

Cf. A031877, A084687, A090056, A090057, A090058, A090059, A090060.