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%I #62 Mar 11 2021 20:44:38
%S 11,15,22,33,44,48,55,66,77,88,99,115,122,124,126,128,155,162,168,175,
%T 184,212,222,244,248,264,288,324,333,336,366,384,396,412,424,444,448,
%U 488,515,555,636,648,666,672,728,777,784,816,824,848,864,888,936,999,1111,1112
%N Numbers that are divisible by each of their digits but that are not divisible by the sum of their digits or by the product of their digits.
%C Numbers which are divisible by the sum and the product of their digits (A038186) are also divisible by each of their digits (A034838)
%C The product of the digits of n are trivially divisible by each digit; so if that product divides n, each digit must divide n. - _Franklin T. Adams-Watters_, Jul 02 2017
%H Robert G. Wilson v, <a href="/A285271/b285271.txt">Table of n, a(n) for n = 1..1520</a>
%e 15 is divisible by its digits 1 and 5, and 15 is divisible by the product of its digits 1*5 = 5, but 15 is not divisible by the sum of its digits 1+5 = 6, hence 15 is a term.
%e 48 is divisible by its digits 4 and 8, and 48 is divisible by the sum of its digits 4+8 = 12, but 48 is not divisible by the product of its digits 4*8 = 32, hence 48 is a term.
%e 124 is divisible by its digits 1, 2 and 4, but 124 is not divisible by the product of its digits 1*2*4 = 8 and 124 is not divisible by the sum of its digits 1+2+4 = 7, hence 124 is a term.
%e 24 is divisible by its digits 2 and 4, and 24 is divisible by the sum of its digits 2+4 = 6, and 24 is also divisible by the product of its digits 2*4 = 8, hence 24 is NOT a term.
%p filter:= proc(n) local F;
%p F:= convert(n,base,10);
%p andmap(t -> t > 0 and n mod t = 0, F) and not(n mod convert(F,`+`) = 0 and n mod convert(F,`*`) = 0)
%p end proc:
%p select(filter, [$11 .. 2000]); # _Robert Israel_, Jul 05 2017
%t fQ[n_] := Block[{ind = IntegerDigits@ n}, Union[ IntegerQ@# & /@ (n/ind)] == {True} && (!IntegerQ[n/Plus @@ ind] || !IntegerQ[n/Times @@ ind])]; Select[Range@ 1112, fQ] (* _Robert G. Wilson v_, Jul 05 2017 *)
%o (PARI) isok(n) = {d = digits(n); if (vecmin(d), for (k=1, #d, if (n % d[k], return (0));); return ((n % vecsum(d)) || (n % prod(k=1, #d, d[k])));); return (0);} \\ _Michel Marcus_, Jul 02 2017
%Y Subsequence of A034838.
%Y Cf. A005349, A007602, A038186.
%K nonn,base
%O 1,1
%A _Bernard Schott_, Jun 24 2017
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