

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
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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



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.


KEYWORD

base,nonn


AUTHOR



STATUS

approved



