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A101170 a(n) divides the number formed by concatenating the sum of the digits of a(n) with a(n). 1

%I #5 Mar 30 2012 17:26:51

%S 1,2,3,4,5,6,7,8,9,10,12,15,18,20,24,25,30,36,40,45,48,50,60,70,75,80,

%T 90,100,120,125,150,180,200,225,240,250,300,360,375,400,450,480,500,

%U 600,700,750,800,900,1000,1125,1200,1250,1500,1800,1875,2000,2250,2400,2500

%N a(n) divides the number formed by concatenating the sum of the digits of a(n) with a(n).

%C The most common factor is 11, which catches most of the trivial cases such as 5000 (which when concatenated with its digit sum yields 55000... 11 * 5000). See A101171 for the first sequence member which uses a new factor.

%C There are only a finite number of terms ending with a nonzero digit. See A101171 for the proof. [From _Max Alekseyev_, May 08 2009]

%e a(50)=1125 because the number formed by concatenating the digit sum of 1125 (9) with 1125 yields a number (91125) that 1125 evenly divides. 91125 / 1125 = 81.

%Y Cf. A101171.

%K base,nonn

%O 1,2

%A Chuck Seggelin (seqfan(AT)plastereddragon.com), Dec 03 2004

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