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A234814 Numbers that are divisible by their digital sum but not by their digital root.

%I A234814 #28 Feb 16 2025 08:33:21
%S A234814 195,209,247,266,285,375,392,407,465,476,481,518,555,592,605,629,644,
%T A234814 645,715,735,736,782,803,825,880,915,935,1066,1095,1148,1168,1183,
%U A234814 1185,1274,1275,1365,1394,1417,1455,1526,1534,1545,1547,1635,1651,1652,1679,1725,1744,1815,1853,1886,1898,1904,1905
%N A234814 Numbers that are divisible by their digital sum but not by their digital root.
%C A234814 These are the Harshad numbers which are missing from A234474.
%H A234814 Reinhard Zumkeller, <a href="/A234814/b234814.txt">Table of n, a(n) for n = 1..10000</a>
%H A234814 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarshadNumber.html">Harshad number</a>.
%e A234814 195 is a term as it is divisible by its digital sum i.e. 15 but not by its digital root i.e. 6.
%t A234814 Select[Range@1905, Mod[#, 1 + Mod[#-1, 9]] > 0 && Mod[#, Plus@@ IntegerDigits@ #] == 0 &] (* _Giovanni Resta_, Jan 03 2014 *)
%o A234814 (C++)
%o A234814 #include<iostream.h>
%o A234814 int digitalsum(int n){int sum=0; while(n>0){sum+=n%10; n/=10;}return(sum);}
%o A234814 int digitalroot(int a){return(1+(a-1)%9);}
%o A234814 int main(){for(int i=1;i<=2000;i++){
%o A234814 if(i%(digitalroot(i))!=0 &&  i%(digitalsum(i))==0) cout<<i<<", ";}}
%o A234814 (Haskell)
%o A234814 a234814 n = a234814_list !! (n-1)
%o A234814 a234814_list = filter (\x -> x `mod` a007953 x == 0 &&
%o A234814                              x `mod` a010888 x /= 0) [1..]
%o A234814 -- _Reinhard Zumkeller_, Mar 04 2014
%Y A234814 Cf. A005349, A234474.
%Y A234814 Cf. A064807, A007953, A010888.
%K A234814 nonn,base
%O A234814 1,1
%A A234814 _Mihir Mathur_, Dec 31 2013