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A337163 Numbers divisible by their individual digits, but not by the product of their digits.

%I A337163 #31 May 06 2022 13:13:51
%S A337163 22,33,44,48,55,66,77,88,99,122,124,126,155,162,168,184,222,244,248,
%T A337163 264,288,324,333,336,366,396,412,424,444,448,488,515,555,636,648,666,
%U A337163 728,777,784,824,848,864,888,936,999,1122,1124,1128,1144,1155,1164,1222
%N A337163 Numbers divisible by their individual digits, but not by the product of their digits.
%C A337163 The sequence is infinite. For example, all numbers of the form ((10^n-1)/9)*(10^2)+24 are terms for n > 0. The numbers of this form will never be divisible by 8 but they will always be divisible by 1, 2 and 4. Also there are infinitely many terms any three of whose consecutive digits are distinct, for example, concatenations of 124. Are there infinitely many terms which don't consist of periodically repeating substrings?  - _Metin Sariyar_, Jan 28 2021
%C A337163 Every repdigit non-repunit with at least 2 digits is a term. - _Bernard Schott_, Jan 28 2021
%H A337163 David A. Corneth, <a href="/A337163/b337163.txt">Table of n, a(n) for n = 1..10000</a>
%e A337163 48 is divisible by 4 and 8, but 48 is not divisible by 4*8 = 32, so 48 is a term.
%e A337163 128 is divisible by 1, 2 and 8, and 128 is divisible by 1*2*8 = 16 with 128 = 16*8, so 128 is not a term.
%t A337163 q[n_] := AllTrue[(digits = IntegerDigits[n]), # > 0 && Divisible[n, #] &] && !Divisible[n, Times @@ digits]; Select[Range[1000], q] (* _Amiram Eldar_, Jan 28 2021 *)
%o A337163 (PARI) isok(n) = my(d=digits(n)); if (vecmin(d), for (i=1, #d, if (n % d[i], return(0))); (n % vecprod(d))); \\ _Michel Marcus_, Jan 28 2021
%Y A337163 Intersection of A034838 and A188643.
%Y A337163 Cf. A087142 (similar, with sum).
%Y A337163 Cf. A087141, A285271.
%K A337163 nonn,base
%O A337163 1,1
%A A337163 _Bernard Schott_, Jan 28 2021
%E A337163 More terms from _Michel Marcus_, Jan 28 2021