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%I #14 Nov 07 2019 07:54:40
%S 1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,24,28,30,36,42,48,60,120
%N Numbers that are divisible by at least one of their digits in every base.
%C This list is probably finite and complete. For example 180 fails at base 23 and 240 fails at bases 21, 31 and 33
%e 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.
%t divQ[n_, base_] := AnyTrue[Select[IntegerDigits[n, base], Positive], Divisible[n, #]&];
%t okQ[n_] := AllTrue[Range[2, n-1], divQ[n, #]&];
%t Select[Range[1000], okQ] (* _Jean-François Alcover_, Nov 07 2019 *)
%Y Cf. A038770, A055239, A055240, A055241, A055242.
%K fini,full,nice,base,nonn
%O 1,2
%A _Henry Bottomley_, May 04 2000
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