A116910 Numbers n such that the number of letters in the Roman numeral for n divides n.

1, 2, 3, 4, 5, 6, 8, 10, 12, 20, 21, 24, 30, 40, 44, 45, 48, 50, 54, 60, 64, 80, 84, 85, 88, 90, 92, 96, 100, 102, 110, 111, 112, 116, 120, 132, 133, 135, 150, 152, 156, 168, 174, 175, 180, 182, 189, 200, 201, 204, 210, 220, 222, 225, 230, 240, 245, 246, 248

Offset

1,2

Links

Nathaniel Johnston and Harvey P. Dale, Table of n, a(n) for n = 1..1000 (* first 593 terms from Nathaniel Johnston *)

Formula

{n such that A006968(n)|n}.

Example

a(23) = 84 because there are 6 letters in LXXXIV and 6 divides 84.
a(44) = 189 because there are 7 letters in CLXXXIX and 7 divides 189.
a(56) = 248 because there are 8 letters in CCXLVIII and 8 divides 248.

Maple

for n from 1 to 500 do if(n mod length(convert(n, roman)) = 0)then printf("%d, ", n): fi: od: # Nathaniel Johnston, May 18 2011

Mathematica

Select[Range[250], Divisible[#, StringLength[IntegerString[#, "Roman"]]]&] (* Harvey P. Dale, Feb 13 2013 *)

Crossrefs

Cf. A006968.

Sequence in context: A238110 A211385 A373194 * A141283 A276828 A309715

Adjacent sequences: A116907 A116908 A116909 * A116911 A116912 A116913

Keyword

base,easy,nonn,less

Author

Jonathan Vos Post, Mar 17 2006

Extensions

Corrected by Nathaniel Johnston, May 18 2011

Status

approved