A090053 Numbers divisible by the number formed when their digits are sorted in ascending order, excluding trivial cases.

105, 108, 405, 510, 540, 702, 703, 810, 1001, 1005, 1008, 1020, 1050, 1080, 2002, 2016, 2025, 2040, 2050, 2100, 3003, 3042, 3060, 3105, 3510, 4004, 4005, 4050, 4080, 4200, 5005, 5010, 5040, 5049, 5100, 5130, 5200, 5400, 6006, 6084

Offset: 1

Author

Chuck Seggelin, Nov 21 2003

Keywords

• base
• nonn

Comments

Trivial cases are identified as (1) values of k where the digits are already in ascending order, like 123 or 2228, such that ASort(k)=k, or (2) values of k where k mod 10 = 0 and all digits other than trailing zeros are in ascending order, like 12000 or 333500, such that ASort(k)=k/10^z, where z = the number of trailing zeros of k. In case (1), k/ASort(k) is equivalent to k/k (as in 123/123). In case (2), k/ASort(k) is 10^z (as in 12000/12). Neither of these cases is very interesting.

Sequence A084687 is a subsequence of this sequence, but that sequence excludes any value of k with 1 or more zero digits.

Examples

			a(1)=105 because the digits of 105 in ascending order are 015 and 105 is divisible by 15. a(24)=3105 because the digits of 3105 in ascending order are 135 and 3105 is divisible by 135.
		

Links

• C. Seggelin, Numbers Divisible by Digit Permutations.

Crossrefs

Cf. A084687, A090055, A090056.