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%I #10 Jan 03 2024 10:44:39
%S 1,2,4,6,720,780,840,1008,1092,1584,2016,2520,2880,3168,3360,3600,
%T 4368,5640,6048,6720,7560,8640,8820,9520,10080,11088,12240,13104,
%U 13440,13860,14040,15840,17160,18480,18720,19320,19656,20736,21840,22176,22680,23040
%N Numbers that are divisible by the sum of their digits in every base from 2 through to 16.
%C Many terms, including the first nine, are in A128397; it seems that the same (and no others(?)) are in A177917. - _M. F. Hasler_, Oct 21 2012
%H Arkadiusz Wesolowski, <a href="/A218087/b218087.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Harshad_number">Harshad number</a>
%e In base 10 the number 322 is divisible by the sum of its digits, it is a Harshad number. It also has this property in octal (322 = 502(8), 5 + 0 + 2 = 7) and hexadecimal (322 = 142(16), 1 + 4 + 2 = 7), but not in binary. Therefore 322 is not a term.
%t lst = {}; Do[b = 2; While[b < 17, If[! Mod[n, Total@IntegerDigits[n, b]] == 0, Break[]]; b++]; If[b == 17, AppendTo[lst, n]], {n, 2, 23040, 2}]; Prepend[lst, 1]
%t Select[Range[25000],Union[Divisible[#,Table[Total[IntegerDigits[#,b]],{b,2,16}]]]=={True}&] (* _Harvey P. Dale_, Jan 03 2024 *)
%Y See A005349 for numbers that are Harshad in base 10.
%K base,nonn
%O 1,2
%A _Arkadiusz Wesolowski_, Oct 20 2012
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