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

Author

Arkadiusz Wesolowski, Oct 20 2012

Keywords

• base
• nonn

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

Examples

			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.
		

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000
• Wikipedia, Harshad number

Crossrefs

See A005349 for numbers that are Harshad in base 10.

Programs

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 *)