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

1,1

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.)

Links

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

C. Seggelin, Numbers Divisible by Digit Permutations.

Example

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

Crossrefs

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

Sequence in context: A112814 A058179 A260461 * A090053 A096093 A378480

Adjacent sequences: A090052 A090053 A090054 * A090056 A090057 A090058

Keyword

base,nonn

Author

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

Status

approved