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

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

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