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Numbers which on division by their digital root give quotient which is divisible by its digital root.
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%I #6 Jan 14 2014 11:43:47

%S 1,2,3,4,5,6,7,8,9,10,12,18,19,20,21,24,27,28,30,36,37,38,40,42,45,46,

%T 50,54,55,56,57,60,63,64,70,72,73,74,76,80,81,82,84,90,91,92,95,100,

%U 108,109,110,111,112,114,118,120,127,128,133,136,138,140,145,146,148,152,154,162,163,164,165,168,171,172

%N Numbers which on division by their digital root give quotient which is divisible by its digital root.

%e 108 is a term as on division by its digital root i.e. 9, gives 12, which is again divisible by its digital root i.e. 3.

%t dr[n_] := 1 + Mod[n-1, 9]; Select[Range@172, IntegerQ[q = #/dr@#] && Mod[q, dr@q] == 0 &] (* _Giovanni Resta_, Jan 14 2014 *)

%K nonn,base,easy

%O 1,2

%A _Mihir Mathur_, Jan 12 2014