A055238 Numbers that are divisible by at least one of their digits in every base.

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

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, n-1], divQ[n, #]&];
Select[Range[1000], okQ] (* Jean-François Alcover, Nov 07 2019 *)

Crossrefs

Cf. A038770, A055239, A055240, A055241, A055242.

Sequence in context: A347933 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