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Numbers that are divisible by their digital sum and digital root.
3

%I #16 Jun 22 2022 11:57:03

%S 1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,30,36,40,42,45,48,50,54,60,63,

%T 70,72,80,81,84,90,100,102,108,110,111,112,114,117,120,126,132,133,

%U 135,140,144,150,152,153,156,162,171,180,190,192,198,200,201,204

%N Numbers that are divisible by their digital sum and digital root.

%C Though a large number of initial terms match, it is different from A005349. First missing term is A005349(57) = 195.

%H Indranil Ghosh, <a href="/A234474/b234474.txt">Table of n, a(n) for n = 1..1000</a>

%e 198 is a term of the sequence as it is divisible by its digital sum i.e., 18 and by its digital root i.e., 9.

%t Select[Range[200],Divisible[#,Total[IntegerDigits[#]] && Divisible[#, #-9*Floor[(#-1)/9]]]&] (* _Indranil Ghosh_, Mar 04 2017 *)

%o (PARI) is(n)=my(d=sumdigits(n)); n%d==0 && n%((d-1)%9+1)==0 \\ _Charles R Greathouse IV_, Dec 26 2013

%Y Intersection of A064807 and A005349.

%Y Cf. A010888, A007953.

%K nonn,base

%O 1,2

%A _Mihir Mathur_, Dec 26 2013