A038367 - OEIS

%I #41 Sep 08 2022 08:44:53

%S 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 101,102,103,104,105,106,107,108,109,110,120,123,130,132,138,140,145,

%U 150,154,159,160,167,170,176,180,183,189,190,195,198,200,201,202,203

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

%C 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 Iain Fox, <a href="/A038367/b038367.txt">Table of n, a(n) for n = 1..10000</a>

%p isA038367 := proc(n)

%p     if type( A007954(n)/A007953(n),'integer') then

%p         true;

%p      else

%p         false;

%p     end if;

%p end proc :

%p for n from 1 to 500 do

%p     if isA038367(n) then

%p         printf("%d,",n) ;

%p     end if;

%p end do: # _R. J. Mathar_, Jun 30 2020

%t okQ[n_]:=Module[{idn=IntegerDigits[n]},Divisible[Times@@idn,Total[idn]]]

%t Select[Range[500],okQ] (* _Harvey P. Dale_, Nov 24 2010 *)

%o (Magma) [0] cat [n: n in [1..250] | IsIntegral(&*Intseq(n)/&+Intseq(n))]; // _Bruno Berselli_, Feb 09 2016

%o (PARI) is(n)=n&&prod(i=1,#n=digits(n),n[i])%vecsum(n)==0 \\ _M. F. Hasler_, Feb 28 2018

%Y See A061013 for case where 0 digits are excluded. Cf. A055931.

%K nonn,base,easy

%O 1,2

%A _Felice Russo_

%E Corrected by _Vladeta Jovovic_ and Larry Reeves (larryr(AT)acm.org), Jun 08 2001

%E Erroneous 0 term removed by _David A. Corneth_, Jun 05 2016