cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A055238 #14 Nov 07 2019 07:54:40
%S A055238 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 A055238 Numbers that are divisible by at least one of their digits in every base.
%C A055238 This list is probably finite and complete. For example 180 fails at base 23 and 240 fails at bases 21, 31 and 33
%e A055238 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 A055238 divQ[n_, base_] := AnyTrue[Select[IntegerDigits[n, base], Positive], Divisible[n, #]&];
%t A055238 okQ[n_] := AllTrue[Range[2, n-1], divQ[n, #]&];
%t A055238 Select[Range[1000], okQ] (* _Jean-François Alcover_, Nov 07 2019 *)
%Y A055238 Cf. A038770, A055239, A055240, A055241, A055242.
%K A055238 fini,full,nice,base,nonn
%O A055238 1,2
%A A055238 _Henry Bottomley_, May 04 2000