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

195, 209, 247, 266, 285, 375, 392, 407, 465, 476, 481, 518, 555, 592, 605, 629, 644, 645, 715, 735, 736, 782, 803, 825, 880, 915, 935, 1066, 1095, 1148, 1168, 1183, 1185, 1274, 1275, 1365, 1394, 1417, 1455, 1526, 1534, 1545, 1547, 1635, 1651, 1652, 1679, 1725, 1744, 1815, 1853, 1886, 1898, 1904, 1905

Offset

1,1

Comments

These are the Harshad numbers which are missing from A234474.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Harshad number.

Example

195 is a term as it is divisible by its digital sum i.e. 15 but not by its digital root i.e. 6.

Mathematica

Select[Range@1905, Mod[#, 1 + Mod[#-1, 9]] > 0 && Mod[#, Plus@@ IntegerDigits@ #] == 0 &] (* Giovanni Resta, Jan 03 2014 *)

Prog

(C++)
#include<iostream.h>
int digitalsum(int n){int sum=0; while(n>0){sum+=n%10; n/=10; }return(sum); }
int digitalroot(int a){return(1+(a-1)%9); }
int main(){for(int i=1; i<=2000; i++){
if(i%(digitalroot(i))!=0 &&  i%(digitalsum(i))==0) cout<<i<<", "; }}
(Haskell)
a234814 n = a234814_list !! (n-1)
a234814_list = filter (\x -> x `mod` a007953 x == 0 &&
                             x `mod` a010888 x /= 0) [1..]
-- Reinhard Zumkeller, Mar 04 2014

Crossrefs

Cf. A005349, A234474.

Cf. A064807, A007953, A010888.

Sequence in context: A296893 A045073 A204811 * A154938 A234100 A336333

Adjacent sequences: A234811 A234812 A234813 * A234815 A234816 A234817

Keyword

nonn,base

Author

Mihir Mathur, Dec 31 2013

Status

approved