cp's OEIS Frontend

A038367 Numbers n with property that (product of digits of n) is divisible by (sum of digits of n).

%I A038367 #41 Sep 08 2022 08:44:53
%S A038367 1,2,3,4,5,6,7,8,9,10,20,22,30,36,40,44,50,60,63,66,70,80,88,90,100,
%T A038367 101,102,103,104,105,106,107,108,109,110,120,123,130,132,138,140,145,
%U A038367 150,154,159,160,167,170,176,180,183,189,190,195,198,200,201,202,203
%N A038367 Numbers n with property that (product of digits of n) is divisible by (sum of digits of n).
%C A038367 Equal to the disjoint union of A061013 and A011540 \ {0}. Contains in particular all positive single-digit integers, those with a digit 0, and 22*{1,...,18}. If x is in the sequence, any digit-permutation of x is also in the sequence. - _M. F. Hasler_, Feb 28 2018
%H A038367 Iain Fox, <a href="/A038367/b038367.txt">Table of n, a(n) for n = 1..10000</a>
%p A038367 isA038367 := proc(n)
%p A038367     if type( A007954(n)/A007953(n),'integer') then
%p A038367         true;
%p A038367      else
%p A038367         false;
%p A038367     end if;
%p A038367 end proc :
%p A038367 for n from 1 to 500 do
%p A038367     if isA038367(n) then
%p A038367         printf("%d,",n) ;
%p A038367     end if;
%p A038367 end do: # _R. J. Mathar_, Jun 30 2020
%t A038367 okQ[n_]:=Module[{idn=IntegerDigits[n]},Divisible[Times@@idn,Total[idn]]]
%t A038367 Select[Range[500],okQ] (* _Harvey P. Dale_, Nov 24 2010 *)
%o A038367 (Magma) [0] cat [n: n in [1..250] | IsIntegral(&*Intseq(n)/&+Intseq(n))]; // _Bruno Berselli_, Feb 09 2016
%o A038367 (PARI) is(n)=n&&prod(i=1,#n=digits(n),n[i])%vecsum(n)==0 \\ _M. F. Hasler_, Feb 28 2018
%Y A038367 See A061013 for case where 0 digits are excluded. Cf. A055931.
%K A038367 nonn,base,easy
%O A038367 1,2
%A A038367 _Felice Russo_
%E A038367 Corrected by _Vladeta Jovovic_ and Larry Reeves (larryr(AT)acm.org), Jun 08 2001
%E A038367 Erroneous 0 term removed by _David A. Corneth_, Jun 05 2016