cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A218087 Numbers that are divisible by the sum of their digits in every base from 2 through to 16.

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%I A218087 #10 Jan 03 2024 10:44:39
%S A218087 1,2,4,6,720,780,840,1008,1092,1584,2016,2520,2880,3168,3360,3600,
%T A218087 4368,5640,6048,6720,7560,8640,8820,9520,10080,11088,12240,13104,
%U A218087 13440,13860,14040,15840,17160,18480,18720,19320,19656,20736,21840,22176,22680,23040
%N A218087 Numbers that are divisible by the sum of their digits in every base from 2 through to 16.
%C A218087 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 A218087 Arkadiusz Wesolowski, <a href="/A218087/b218087.txt">Table of n, a(n) for n = 1..10000</a>
%H A218087 Wikipedia, <a href="http://en.wikipedia.org/wiki/Harshad_number">Harshad number</a>
%e A218087 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 A218087 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 A218087 Select[Range[25000],Union[Divisible[#,Table[Total[IntegerDigits[#,b]],{b,2,16}]]]=={True}&] (* _Harvey P. Dale_, Jan 03 2024 *)
%Y A218087 See A005349 for numbers that are Harshad in base 10.
%K A218087 base,nonn
%O A218087 1,2
%A A218087 _Arkadiusz Wesolowski_, Oct 20 2012