

A055238


Numbers that are divisible by at least one of their digits in every base.


4



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 24, 28, 30, 36, 42, 48, 60, 120
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OFFSET

1,2


COMMENTS

This list is probably finite and complete. For example 180 fails at base 23 and 240 fails at bases 21, 31 and 33


LINKS

Table of n, a(n) for n=1..24.


EXAMPLE

9 is included because it can be written as 111111111,1001,100,21,14,13,12,11,10 or 9 and in every case there is a digit which divides 9; 11 is not on the list because in base 4 it is written 23 and 11 is not divisible by either 2 or 3.


MATHEMATICA

divQ[n_, base_] := AnyTrue[Select[IntegerDigits[n, base], Positive], Divisible[n, #]&];
okQ[n_] := AllTrue[Range[2, n1], divQ[n, #]&];
Select[Range[1000], okQ] (* JeanFrançois Alcover, Nov 07 2019 *)


CROSSREFS

Cf. A038770, A055239, A055240, A055241, A055242.
Sequence in context: A243356 A117296 A096503 * A100952 A303332 A030477
Adjacent sequences: A055235 A055236 A055237 * A055239 A055240 A055241


KEYWORD

fini,full,nice,base,nonn


AUTHOR

Henry Bottomley, May 04 2000


STATUS

approved



