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A090053 Numbers divisible by the number formed when their digits are sorted in ascending order, excluding trivial cases. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..40.

C. Seggelin, Numbers Divisible by Digit Permutations.

EXAMPLE

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.

CROSSREFS

Cf. A084687, A090055, A090056.

Sequence in context: A058179 A260461 A090055 * A096093 A179142 A039553

Adjacent sequences:  A090050 A090051 A090052 * A090054 A090055 A090056

KEYWORD

base,nonn

AUTHOR

Chuck Seggelin (barkeep(AT)plastereddragon.com), Nov 21 2003

STATUS

approved

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Last modified August 13 06:25 EDT 2022. Contains 356078 sequences. (Running on oeis4.)