A342445 - OEIS

%I #35 Jan 16 2025 16:05:43

%S 22,33,44,48,55,66,77,88,99,122,124,126,155,162,168,184,202,204,222,

%T 244,248,264,280,288,303,324,330,333,336,366,396,404,408,412,420,424,

%U 440,444,448,488,505,515,555,606,636,648,660,666,707,728,770,777,784,808,824,840

%N Numbers that are divisible by their nonzero digits but are not divisible by the product of their nonzero digits.

%C Numbers that are divisible by the product of their nonzero digits (A055471) are trivially divisible by each of their nonzero digits (A002796), but the converse is false. This sequence = A002796 \ A055471 and consists of these counterexamples.

%C This sequence differs from A337163: the first sixteen terms are the same but a(17) = 202 while A337163(17) = 222.

%H Harvey P. Dale, <a href="/A342445/b342445.txt">Table of n, a(n) for n = 1..2000</a>

%e 204 is divisible by 2 and 4 but 204 is not divisible by 2*4 = 8, hence 204 is a term.

%e 248 is divisible by 2, by 4 and by 8 but 248 is not divisible by 2*4*8 = 64, hence 248 is a term.

%t q[n_] := AllTrue[(d = Select[IntegerDigits[n], # > 0 &]), Divisible[n, #] &] && ! Divisible[n, Times @@ d]; Select[Range[840], q] (* _Amiram Eldar_, Mar 21 2021 *)

%t dnzQ[n_]:=With[{c=DeleteCases[IntegerDigits[n],0]},Union[Boole[Divisible[n,c]]]=={1}&&!Divisible[n,Times@@c]]; Select[ Range[ 1000],dnzQ] (* _Harvey P. Dale_, Jan 16 2025 *)

%o (PARI) isok(m) = my(d=select(x->(x != 0), digits(m))); (m % vecprod(d)) && (sum(k=1, #d, m % d[k]) == 0); \\ _Michel Marcus_, Mar 22 2021

%Y Equals A002796 \ A055471.

%Y Cf. A337163 = A034838 \ A007602 (subsequence of zeroless numbers).

%K nonn,base

%O 1,1

%A _Bernard Schott_, Mar 20 2021