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 A218087 Numbers that are divisible by the sum of their digits in every base from 2 through to 16. 3
 1, 2, 4, 6, 720, 780, 840, 1008, 1092, 1584, 2016, 2520, 2880, 3168, 3360, 3600, 4368, 5640, 6048, 6720, 7560, 8640, 8820, 9520, 10080, 11088, 12240, 13104, 13440, 13860, 14040, 15840, 17160, 18480, 18720, 19320, 19656, 20736, 21840, 22176, 22680, 23040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000 Wikipedia, Harshad number EXAMPLE 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. MATHEMATICA 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] Select[Range[25000], Union[Divisible[#, Table[Total[IntegerDigits[#, b]], {b, 2, 16}]]]=={True}&] (* Harvey P. Dale, Jan 03 2024 *) CROSSREFS See A005349 for numbers that are Harshad in base 10. Sequence in context: A345092 A033319 A185151 * A090315 A083753 A170807 Adjacent sequences: A218084 A218085 A218086 * A218088 A218089 A218090 KEYWORD base,nonn AUTHOR Arkadiusz Wesolowski, Oct 20 2012 STATUS approved

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Last modified July 12 23:13 EDT 2024. Contains 374257 sequences. (Running on oeis4.)