

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]


CROSSREFS

See A005349 for numbers that are Harshad in base 10.
Sequence in context: A066719 A033319 A185151 * A090315 A083753 A170807
Adjacent sequences: A218084 A218085 A218086 * A218088 A218089 A218090


KEYWORD

base,nonn


AUTHOR

Arkadiusz Wesolowski, Oct 20 2012


STATUS

approved



